CN111687821B - Rotary parallel flying mechanical arm system and expected rotation angle calculating method - Google Patents

Rotary parallel flying mechanical arm system and expected rotation angle calculating method Download PDF

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CN111687821B
CN111687821B CN202010589808.3A CN202010589808A CN111687821B CN 111687821 B CN111687821 B CN 111687821B CN 202010589808 A CN202010589808 A CN 202010589808A CN 111687821 B CN111687821 B CN 111687821B
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mechanical arm
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angle
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CN111687821A (en
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李湛
刘金辉
杨学博
高会军
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Harbin Institute of Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • B25J9/0045—Programme-controlled manipulators having parallel kinematics with kinematics chains having a rotary joint at the base
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1612—Programme controls characterised by the hand, wrist, grip control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
    • B25J9/1623—Parallel manipulator, Stewart platform, links are attached to a common base and to a common platform, plate which is moved parallel to the base
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1651—Programme controls characterised by the control loop acceleration, rate control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C1/00—Fuselages; Constructional features common to fuselages, wings, stabilising surfaces or the like
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C27/00—Rotorcraft; Rotors peculiar thereto
    • B64C27/04—Helicopters
    • B64C27/08—Helicopters with two or more rotors
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64F—GROUND OR AIRCRAFT-CARRIER-DECK INSTALLATIONS SPECIALLY ADAPTED FOR USE IN CONNECTION WITH AIRCRAFT; DESIGNING, MANUFACTURING, ASSEMBLING, CLEANING, MAINTAINING OR REPAIRING AIRCRAFT, NOT OTHERWISE PROVIDED FOR; HANDLING, TRANSPORTING, TESTING OR INSPECTING AIRCRAFT COMPONENTS, NOT OTHERWISE PROVIDED FOR
    • B64F5/00—Designing, manufacturing, assembling, cleaning, maintaining or repairing aircraft, not otherwise provided for; Handling, transporting, testing or inspecting aircraft components, not otherwise provided for

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Abstract

A rotary parallel flying mechanical arm system and an expected rotation angle calculating method belong to the field of robot aerial manipulators. The invention aims to solve the problems of low load capacity, low precision and low running speed of the conventional series-connection type flying mechanical arm. The system comprises: the four-rotor aircraft comprises four rotor aircrafts, a parallel mechanical arm mechanism, a centralized control module and an execution mechanism, wherein the centralized control module is arranged in the center of the lower surface of each four rotor aircraft; the head end of the parallel mechanical arm mechanism is connected with the four-rotor aircraft, and the tail end of the parallel mechanical arm mechanism is detachably connected with the execution mechanism; the parallel mechanical arm mechanism has a six-degree-of-freedom rotatable structure and can drive the actuating mechanism to reach a task point at an expected pose. The invention can realize aerial operation of complex operation.

Description

Rotary parallel flying mechanical arm system and expected rotation angle calculating method
Technical Field
The invention relates to a rotary parallel flying mechanical arm system and an expected rotation angle calculating method, and belongs to the field of robot aerial manipulators.
Background
With the continuous development of science and technology, unmanned aerial vehicles have been widely used in non-contact application occasions such as aerial photography investigation, electric power inspection, pesticide spraying. However, a pure drone is difficult to be qualified for tasks that are complex, such as flight grabbing, and require active operation. In recent years, researchers have attempted to mount robotic arms on aircraft to form flying robotic arm systems. The measure greatly expands the working range and flexibility of the robot and enriches the operation types, thereby having wide application prospect.
According to different mechanical arm structures, the flying mechanical arm can be divided into a series flying mechanical arm and a parallel flying mechanical arm. The existing flying mechanical arms are basically in series connection, and have the advantages of low cost, simple structure, large working range and the like, and related research is abundant. For example, in the existing flying mechanical arm with a flexible grabber, a multi-rotor aircraft, a multi-degree-of-freedom serial mechanical arm and the flexible grabber are sequentially connected, so that the multi-rotor aircraft, the multi-degree-of-freedom serial mechanical arm and the flexible grabber can adapt to the appearance of a target object, and the success rate of grabbing tasks is improved. In addition, in the existing grabbing operation-oriented rotor flight mechanical arm system, a seven-degree-of-freedom redundant mechanical arm is mounted on a six-rotor aircraft, and an under-actuated flexible paw is mounted at the tail end of the seven-degree-of-freedom redundant mechanical arm, so that the flexibility of operation is further improved, and the rapid object capturing and carrying task is facilitated.
However, the above-mentioned tandem type flying robot system can perform only some simple tasks such as flying to grab, move light objects, and has disadvantages of low load capacity, low precision, slow operation speed, etc., thus limiting its application in the field where a large force or torque needs to be applied to the outside, for example, on a high voltage power line instead of manually grabbing a hammer to strike a part to be reinforced.
There is another potential application scenario for flying arm systems: and (4) shooting at a short distance. The appearance of the holder solves the problem that the attitude angle of the airborne camera needs to be adjusted in real time. But because the cloud platform degree of freedom is lower, when unmanned aerial vehicle position produced small disturbance because environmental impact, the skew also can take place for the camera to the effect of shooting closely is influenced. There is a need for a robotic mechanism that can adjust both the attitude angle of the camera and the position of the camera in real time based on the disturbances.
Disclosure of Invention
The invention provides a rotary parallel flying mechanical arm system and an expected rotation angle calculating method, aiming at the problems of low load capacity, low precision and low running speed of the existing series flying mechanical arm.
The invention provides a rotary parallel type flying mechanical arm system, which comprises a four-rotor aircraft, a parallel mechanical arm mechanism, a centralized control module 3 and an actuating mechanism 15,
a centralized control module 3 is arranged in the center of the lower surface of the four-rotor aircraft; the head end of the parallel mechanical arm mechanism is connected with the four-rotor aircraft, and the tail end of the parallel mechanical arm mechanism is detachably connected with the executing mechanism 15;
the parallel mechanical arm mechanism has a six-degree-of-freedom rotatable structure, and can drive the actuating mechanism 15 to reach a task point in a desired pose.
According to the rotary parallel type flying robot system of the present invention, the four-rotor aircraft includes a propeller 1, a brushless motor 2, a horn 4 and a gyroplane chassis 5,
the four machine arms 4 are connected into a cross structure; the upper surface of the tail end of each machine arm 4 is fixedly provided with a brushless motor 2, and an output shaft of each brushless motor 2 is provided with a propeller 1; four arms 4 connected by a cross structure are fixed on the upper surface of a rotorcraft chassis 5 in the center; a centralized control module 3 is arranged at the center of the lower surface of a gyroplane chassis 5; the gyroplane chassis 5 is of a regular hexagon structure.
According to the rotary parallel type flying mechanical arm system of the invention, the parallel mechanical arm mechanism comprises a support column 6, a parallel mechanical arm fixed platform 7, a direct current servo motor 8, a two-degree-of-freedom connecting mechanism 9, a motor rocker arm 10, a connecting rod 11, a three-degree-of-freedom connecting mechanism 12 and a parallel mechanical arm moving platform 13,
the parallel mechanical arm fixed platform 7 is of a regular hexagon structure, has the same size as the gyroplane chassis 5, and is coaxially configured; the parallel mechanical arm fixed platform 7 is connected with the gyroplane chassis 5 through six support columns 6 which are uniformly distributed;
the parallel mechanical arm fixed platform 7 is provided with a direct current servo motor 8 corresponding to each side, and the rotating plane of each direct current servo motor 8 is vertical to the corresponding side of the parallel mechanical arm fixed platform 7; the output shaft of each direct current servo motor 8 is sleeved in the protruding end of a motor rocker arm 10, the tail end of the motor rocker arm 10 is connected with the head end of a connecting rod 11 through a two-degree-of-freedom connecting mechanism 9, and the tail end of each connecting rod 11 is connected with a parallel mechanical arm moving platform 13 through a three-degree-of-freedom connecting mechanism 12; the connection points of the six three-degree-of-freedom connecting mechanisms 12 and the parallel mechanical arm movable platform 13 are in a common circle;
the parallel mechanical arm fixed platform 7 is provided with a gap corresponding to each edge, and each motor rocker arm 10 can drive the corresponding two-degree-of-freedom connecting mechanism 9 to penetrate through one gap under the driving of the direct current servo motor 8, so that the actuating mechanism 15 is driven to change the pose.
According to the rotary parallel type flying mechanical arm system of the invention, the notch comprises a rectangular notch; each rectangular notch is perpendicular to the corresponding side of the parallel mechanical arm fixed platform 7;
the direct current servo motor 8 is positioned in an included angle between the corresponding side of the parallel mechanical arm fixed platform 7 and the long side of the rectangular notch and is close to the edge of the corresponding side of the parallel mechanical arm fixed platform 7;
the adjacent rectangular gaps are overlapped after the parallel mechanical arm fixed platform 7 rotates for 60 degrees.
According to the rotary parallel flying mechanical arm system, the two-degree-of-freedom connecting mechanism 9 and the three-degree-of-freedom connecting mechanism 12 have the same structure and respectively comprise a male hinge 16, a cross shaft 17 and a female hinge 18; one shaft of the cross shaft 17 is rotatably connected with the male hinge 16, and the other shaft of the cross shaft 17 is rotatably connected with the female hinge 18;
in the two-degree-of-freedom connecting mechanism 9, a male hinge 16 is fixed in a concave hole at the tail end of a motor rocker arm 10, so that the male hinge 16 cannot rotate; the female hinge 18 is connected with the head end of the connecting rod 11;
in the three-degree-of-freedom connecting mechanism 12, a female hinge 18 is connected with the tail end of the connecting rod 11, and a male hinge 16 is arranged in a through hole correspondingly arranged on the parallel mechanical arm moving platform 13 and is rotatably connected with the parallel mechanical arm moving platform 13.
According to the rotary parallel type flying mechanical arm system, the centralized control module 3 comprises a gyroplane integrated module and a parallel mechanical arm control module;
the gyroplane integration module comprises a power supply module, a sensor module and a flight controller module, wherein the power supply module is used for providing working power supply for the four-rotor aircraft, the sensor module is used for acquiring the motion state of the four-rotor aircraft in real time, and the flight controller module is used for controlling the four-rotor aircraft to run according to aircraft control signals or an expected track of the aircraft;
the parallel mechanical arm control module comprises a power supply, a main control board and a signal transceiving device, wherein the power supply is used for providing a working power supply for the parallel mechanical arm mechanism, the main control board is used for controlling the pose of the tail end of the parallel mechanical arm mechanism according to a mechanical arm control signal or an expected track of the tail end of the mechanical arm, and the main control board is interacted with the ground station through the signal transceiving device;
the parallel mechanical arm mechanism further comprises a tail end sensor module, wherein the tail end sensor module is fixed at the center of the parallel mechanical arm moving platform 13 and used for acquiring the current motion state of the tail end of the parallel mechanical arm mechanism in real time.
According to the rotary parallel type flying robot system of the present invention, the actuator 15 includes an actuator claw or an aerial camera;
when the executing mechanism 15 is an executing paw, the executing paw is driven by the steering engine 14.
The invention also provides a method for calculating the expected rotation angle of the rotary parallel flying mechanical arm system, which is realized based on the rotary parallel flying mechanical arm system, and the calculating method comprises the following steps:
the method comprises the following steps: acquiring the motion state of the four-rotor aircraft and the current motion state of the tail end of the parallel mechanical arm mechanism, and calculating to obtain a rotation matrix of the four-rotor aircraft;
step two: the flight controller module controls the four-rotor aircraft to reach a preset range of a task point according to the current motion state;
step three: the ground station plans the expected track of the tail end of the mechanical arm according to the operation requirement and sends the expected track to the main control board through the signal receiving and sending device;
step four: according to the vector relation, an inverse kinematics model of the parallel mechanical arm mechanism is established, and the end pose of the mechanical arm required by the current task point in the expected track of the end of the mechanical arm is converted into the virtual rod length between the equivalent rotating point on the motor shaft of the direct current servo motor 8 and the connecting point of the parallel mechanical arm movable platform 13;
step five: resolving the virtual rod length into an expected rotation angle of the direct current servo motor 8;
step six: the parallel mechanical arm control module controls the corresponding direct current servo motor 8 to rotate to a desired rotation angle, and controls the actuating mechanism 15 to act.
According to the desired rotation angle calculating method of the rotary parallel type flying robot system of the present invention,
in step one, the four rotors flyThe rotation matrix of the line driving device in the inertial coordinate system is R1：
Figure BDA0002555939110000041
Wherein c represents cosine operation and s represents sine operation;
Figure BDA0002555939110000042
representing the roll angle, theta, of a four-rotor aircraft1Representing the pitch angle, psi, of a four-rotor aircraft1Representing the yaw angle of a four-rotor aircraft;
euler angle phi1Comprises the following steps:
Figure BDA0002555939110000043
the rotation matrix of the tail end of the parallel mechanical arm mechanism under the inertial coordinate system is R2；
Corresponding Euler angle phi2Comprises the following steps:
Figure BDA0002555939110000044
Figure BDA0002555939110000045
representing the roll angle, theta, of the end of the parallel robot arm mechanism2Indicating the pitch angle, psi, of the end of the parallel-connected robot arm mechanism2Indicating a yaw angle of the end of the parallel mechanical arm mechanism;
in step three, the planning of the expected trajectory of the end of the mechanical arm comprises:
under the point-to-point working mode, the ground station carries out cubic polynomial interpolation between the current pose and the target pose of the tail end of the mechanical arm to obtain the expected coordinate P of the tail end of the mechanical arm under an inertial coordinate system2dAnd desired Euler angle phi2d；
The rotation matrix R of the desired trajectory2dComprises the following steps:
Figure BDA0002555939110000046
Figure BDA0002555939110000047
roll angle, θ, representing a desired trajectory of the end of the parallel-connected robotic arm mechanism2dPitch angle, psi, representing a desired trajectory of the end of the parallel robot2dA yaw angle representing a desired trajectory of the end of the parallel linkage mechanical arm mechanism;
calculating the coordinate P of the expected track point at the tail end of the mechanical arm in a machine body coordinate system: p ═ P2d-P1(ii) a In the formula P1Representing the coordinates of the four-rotor aircraft in an inertial coordinate system; then the rotation matrix R of the expected track point at the end of the mechanical arm in the body coordinate system is:
Figure BDA0002555939110000051
and sending the rotation matrix R to a main control board through a signal receiving and sending device.
According to the desired rotation angle calculating method of the rotary parallel type flying robot system of the present invention,
in the fourth step, the center of the cross shaft 17 of the two-degree-of-freedom connecting mechanism 9 is moved to the corresponding motor shaft along the direction of the corresponding motor rocker arm 10 to obtain the equivalent rotating point Bi(ii) a The six equivalent rotation points are in a common circle;
six equivalent rotation points BiDenoted b in the body coordinate systemi：
bi＝[rb cosδi rb sinδi h]T，
Wherein i is 1, 2, 3, … …, 6;
in the formula rbIs an equivalent rotation point BiDistance, delta, to the center of the circle in which the six equivalent points of rotation lieiIs an equivalent rotation point BiA rotation angle corresponding to the connection line of the centers of the circles of the six equivalent rotation points, h is the distance between the plane of the six equivalent rotation points and the XOY plane of the coordinate system of the machine body；
Similarly, six connecting points C on the parallel mechanical arm moving platform 13 are connectediDenoted c in the robot arm end coordinate systemi：
ci＝[rccosγi rcsinγi 0]T，
In the formula rcIs a connection point CiDistance, gamma, to the center of the circle in which the six points of connection lieiIs a connection point CiThe rotating angle corresponds to a connecting line of the centers of the circles where the six connecting points are located;
b is to beiAnd CiAfter connection to obtain
Figure BDA0002555939110000052
Expressed as l in the body coordinate systemi：
li＝P+Rci-bi， (3)
And (3) carrying out modulus operation on the formula (3) to establish an inverse kinematics model of the parallel mechanical arm mechanism, so that the length | l of the virtual rodiI is:
Figure BDA0002555939110000053
in step five, the compound is treated with BiEstablishing a resolving coordinate system for the origin, wherein the coordinate axis direction of the resolving coordinate system is the same as that of the machine body coordinate system; b isiJiRepresenting a motor rocker arm 10, C of length piJiRepresenting a connecting rod 11, alpha, of length qiDesired angle of rotation, beta, of the motor to be solvediIs a rotation plane of the DC servo motor 8 and XB in resolving coordinatesiThe included angle formed by the Z plane is formed,
the center J of the cross 17 of the two-degree-of-freedom connection 9iThe coordinates in the solved coordinate system are expressed as:
Figure BDA0002555939110000061
to make the virtual rod longQuantity liThe three-axis components under the resolving coordinate system are respectively marked as lix、liy、lizAccording to the cosine theorem, the following results are obtained:
Figure BDA0002555939110000062
to simplify the expression, the following variable substitutions are made:
Figure BDA0002555939110000063
according to the auxiliary angle formula, the following results are obtained:
Figure BDA0002555939110000064
then solve for alphaiTo obtain two solutions alpha of the desired rotation anglei1And alphai2：
Figure BDA0002555939110000065
And selecting one solution closest to the current rotation angle of the DC servo motor 8 as the expected rotation angle.
The invention has the beneficial effects that: the invention can realize aerial operation of complex operation. The system has the advantages of strong bearing capacity, high precision, high speed, high rigidity and the like, and is suitable for complex operation in a contact environment.
According to the system, the rotary six-degree-of-freedom parallel type flying mechanical arm is arranged on the rotor craft, so that the tail end of the mechanical arm can reach a task point in a proper pose in a working range, the flexibility of the rotor craft is expanded, the stability and the efficiency during operation are improved, and the system can be competent for complex operation tasks in contact with an external environment. Meanwhile, the parallel flying mechanical arm can effectively compensate pose disturbance of the rotor craft, so that the rotor craft can obtain a better effect in a close-range shooting task.
Compared with a series-connection type flying mechanical arm, the constraint of the parallel structure enables the mechanical arm to provide higher load and pose accuracy, high-speed acceleration is allowed to be executed, the inverse kinematics solution form is simple, the solution is convenient, and the practical application of the solution method is facilitated.
The tail end actuating mechanism adopts a modular design concept, is convenient to install and disassemble, can replace different tail end actuating devices at any time according to task types, and widens the application range of the invention.
Drawings
Fig. 1 is a schematic structural view of a rotary parallel type flying robot system according to the present invention;
FIG. 2 is a schematic diagram of a parallel robot stage;
FIG. 3 is a schematic structural diagram of a two-degree-of-freedom linkage mechanism and a three-degree-of-freedom linkage mechanism;
FIG. 4 is a schematic representation of the geometric relationship between virtual bar lengths, motor rockers, and links of parallel robotic arms.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
First embodiment, referring to fig. 1, a first aspect of the present invention provides a rotary parallel type flying robot system, which includes a quadrotor aircraft, a parallel robot mechanism, a centralized control module 3, and an actuator 15,
a centralized control module 3 is arranged in the center of the lower surface of the four-rotor aircraft; the head end of the parallel mechanical arm mechanism is connected with the four-rotor aircraft, and the tail end of the parallel mechanical arm mechanism is detachably connected with the executing mechanism 15;
the parallel mechanical arm mechanism has a six-degree-of-freedom rotatable structure, and can drive the actuating mechanism 15 to reach a task point in a desired pose.
Further, as shown in fig. 1, the quad-rotor aircraft includes a propeller 1, a brushless motor 2, a horn 4 and a gyroplane chassis 5,
the four machine arms 4 are connected into a cross structure and are a part of a machine frame with 700-axle distance; the upper surface of the tail end of each machine arm 4 is fixedly provided with a brushless motor 2, and an output shaft of each brushless motor 2 is provided with a propeller 1; four arms 4 connected by a cross structure are fixed on the upper surface of a rotorcraft chassis 5 in the center; a centralized control module 3 is arranged at the center of the lower surface of a gyroplane chassis 5; the gyroplane chassis 5 is of a regular hexagon structure.
In this embodiment, the horn 4 and the rotorcraft chassis 5 form a frame, which is the basic structure that carries the entire system. Wherein two adjacent machine arms 4 are perpendicular to each other; the size of the gyroplane chassis 5 is not less than that of the parallel mechanical arm fixed platform 7, and can be equal to the peripheral size of the parallel mechanical arm fixed platform 7.
Each brushless motor 2 is connected with an electronic governor. The propeller 1, the brushless motor 2 and the electronic governor constitute a power module.
Further, as shown in fig. 1, the parallel mechanical arm mechanism includes a support column 6, a parallel mechanical arm fixed platform 7, a dc servo motor 8, a two-degree-of-freedom connecting mechanism 9, a motor rocker 10, a connecting rod 11, a three-degree-of-freedom connecting mechanism 12, and a parallel mechanical arm moving platform 13,
the parallel mechanical arm fixed platform 7 is of a regular hexagon structure, has the same size as the gyroplane chassis 5, and is coaxially configured; the parallel mechanical arm fixed platform 7 is connected with the gyroplane chassis 5 through six support columns 6 which are uniformly distributed;
the parallel mechanical arm fixed platform 7 is provided with a direct current servo motor 8 corresponding to each side, and the rotating plane of each direct current servo motor 8 is vertical to the corresponding side of the parallel mechanical arm fixed platform 7; the output shaft of each direct current servo motor 8 is sleeved in the protruding end of a motor rocker arm 10, the tail end of the motor rocker arm 10 is connected with the head end of a connecting rod 11 through a two-degree-of-freedom connecting mechanism 9, and the tail end of each connecting rod 11 is connected with a parallel mechanical arm moving platform 13 through a three-degree-of-freedom connecting mechanism 12; the connection points of the six three-degree-of-freedom connecting mechanisms 12 and the parallel mechanical arm movable platform 13 are in a common circle;
the parallel mechanical arm fixed platform 7 is provided with a gap corresponding to each edge, and each motor rocker arm 10 can drive the corresponding two-degree-of-freedom connecting mechanism 9 to penetrate through one gap under the driving of the direct current servo motor 8, so that the actuating mechanism 15 is driven to change the pose.
Support column 6 supports between parallel mechanical arm fixed platform 7 and gyroplane chassis 5 to evenly distributed is in 5 edges on gyroplane chassis, is used for fixing parallel mechanical arm fixed platform 7 in four gyroplane below, for centralized control module 3's installation to and parallel mechanical arm mechanism's motion provides the space.
The system comprises six groups of direct current servo motors 8, six motor rocker arms 10, six connecting rods 11, a connecting mechanism, a fixed platform and a movable platform. In order to reduce the cost, the direct current servo motor 8 can be replaced by a steering engine, six groups of motors are sequentially arranged on the edge of each edge of the regular hexagon fixed platform, and the rotation plane of each motor is perpendicular to the corresponding edge of the fixed platform. The parallel mechanical arm moving platform 13 can be selected to be circular, so that the system is restrained. Six through holes can be formed in the parallel mechanical arm moving platform 13 and used for installing the male hinges 16 of the three-degree-of-freedom connecting mechanism 12, and the centers of the six through holes are in a common circle.
Each direct current servo motor 8 is provided with an encoder as a basis of feedback control, the installation position of the direct current servo motor 8 is tightly attached to and connected with the corresponding edge of the fixed platform 7 of the mechanical arm and the long edge of the rectangle, and the rotation plane of the direct current servo motor 8 is perpendicular to the corresponding edge of the fixed platform.
Still further, as shown in fig. 1 and 2, the notch includes a rectangular notch; each rectangular notch is perpendicular to the corresponding side of the parallel mechanical arm fixed platform 7;
the direct current servo motor 8 is positioned in an included angle between the corresponding side of the parallel mechanical arm fixed platform 7 and the long side of the rectangular notch and is close to the edge of the corresponding side of the parallel mechanical arm fixed platform 7;
the adjacent rectangular gaps are overlapped after the parallel mechanical arm fixed platform 7 rotates for 60 degrees.
The top view of the parallel mechanical arm fixed platform 7 is shown in fig. 2, each side of the parallel mechanical arm fixed platform is cut into a rectangle which is slightly larger than the total size of the two-degree-of-freedom connecting mechanism 9 and the motor rocker arm 10, so that the motor rocker arm 10 can normally rotate to the position above the parallel mechanical arm fixed platform 7, and the working range of the parallel mechanical arm is effectively expanded.
In the invention, the rotor craft and the parallel mechanical arm can be connected by adopting a pillar structure, the module follows the integrated thought, and the fixed platform is cut according to the rectangle, so that the rocker arm of the mechanical arm can rotate to the upper part of the fixed platform of the mechanical arm, thereby expanding the working range of the mechanical arm.
Still further, as shown in fig. 3, the two-degree-of-freedom connecting mechanism 9 and the three-degree-of-freedom connecting mechanism 12 have the same structure, and both include a male hinge 16, a cross 17, and a female hinge 18; one shaft of the cross shaft 17 is rotatably connected with the male hinge 16, and the other shaft of the cross shaft 17 is rotatably connected with the female hinge 18;
the two-degree-of-freedom connecting mechanism 9 has an equivalent effect of a Hooke hinge, wherein a male hinge 16 is fixed in a sunken hole at the tail end of the motor rocker arm 10, so that the male hinge 16 cannot rotate, and a female hinge 18 is connected with the head end of a connecting rod 11;
the three-degree-of-freedom connecting mechanism 12 has an equivalent function of a spherical hinge, wherein the female hinge 18 is connected with the tail end of the connecting rod 11, and the male hinge 16 is arranged in a through hole correspondingly arranged on the parallel mechanical arm moving platform 13 and is rotatably connected with the parallel mechanical arm moving platform 13.
Still further, as shown in fig. 1, the centralized control module 3 includes a rotorcraft integration module and a parallel mechanical arm control module;
the gyroplane integration module comprises a power supply module, a sensor module and a flight controller module, wherein the power supply module is used for providing working power supply for the four-rotor aircraft, the sensor module is used for acquiring the motion state of the four-rotor aircraft in real time, and the flight controller module is used for controlling the four-rotor aircraft to run according to aircraft control signals or an expected track of the aircraft;
the parallel mechanical arm control module comprises a power supply, a main control board and a signal transceiving device, wherein the power supply is used for providing a working power supply for the parallel mechanical arm mechanism, the main control board is used for controlling the pose of the tail end of the parallel mechanical arm mechanism according to a mechanical arm control signal or an expected track of the tail end of the mechanical arm, and the main control board is interacted with the ground station through the signal transceiving device;
the parallel mechanical arm mechanism further comprises a tail end sensor module, wherein the tail end sensor module is fixed at the center of the parallel mechanical arm moving platform 13 and used for acquiring the current motion state of the tail end of the parallel mechanical arm mechanism in real time.
The power module, the sensor module and the flight controller module are integrated in the center of the lower portion of the rotor craft chassis, and therefore the motion of the parallel mechanical arm rocker arm is not affected. The flight controller module receives a remote control signal sent by a user or an expected track planned by the ground workstation to control the operation of the power module.
And the main control board of the parallel mechanical arm control module receives the expected track of the mechanical arm sent by the ground workstation and controls the tail end of the mechanical arm to reach the corresponding pose.
The sensor modules of the gyroplane integration module can comprise a GPS, a barometer, a three-axis accelerometer, a three-axis gyroscope, a three-axis magnetometer and other devices capable of acquiring the pose of the quadrotor in real time.
The centralized control module 3 should limit the size of the fixed platform not to exceed the inscribed circle of the parallel mechanical arm fixed platform 7, so that the motor rocker arm 10 can rotate to the upper part of the fixed platform without obstruction.
Still further, as shown in fig. 1, the actuator 15 includes an actuator gripper or an aerial camera;
when the executing mechanism 15 is an executing paw, the executing paw is driven by the steering engine 14. When the operating task is carried out, the tail end execution paw is driven by the steering engine and is converted into the open-close state of the two fingers paw through the gear transmission mechanism sleeved on the output shaft of the steering engine. In the active operation task, the tail end execution paw can be connected with the parallel mechanical arm-moving platform through a detachable structure such as a bolt.
And when the aerial photography task is carried out, the tail end execution paw is detached and replaced by an aerial photography camera which is fixed on and connected with the mechanical arm moving platform.
As an example, the terminal execution paw is driven by the steering engine 14, a gear transmission mechanism of the terminal execution paw is connected with an output shaft of the steering engine 14, and the opening degree of the terminal execution paw can be adjusted by the rotation of the steering engine 14.
The system of the invention can be further improved as follows:
1) higher rotor count aircraft are employed to increase loading.
2) Aiming at the operation with low precision requirement, the steering engine is used for replacing a direct current servo motor so as to save cost.
3) Depending on the task type, a more suitable working device is selected to replace the end effector gripper.
4) The two-degree-of-freedom connecting mechanism and the three-degree-of-freedom connecting mechanism which are more space-saving and wider in moving range are adopted.
In a second embodiment, referring to fig. 1 to 4, another aspect of the present invention provides a method for calculating a desired rotation angle of a rotating parallel type flying robot system, where the method is implemented based on a first embodiment, and the method includes:
the method comprises the following steps: acquiring the motion state of the four-rotor aircraft and the current motion state of the tail end of the parallel mechanical arm mechanism, and calculating to obtain a rotation matrix of the four-rotor aircraft; in the first step, an Euler angle representation method of a four-rotor aircraft is converted into rotation matrix representation;
step two: the flight controller module controls the four-rotor aircraft to reach a preset range of a task point according to the current motion state;
step three: the ground station plans the expected track of the tail end of the mechanical arm according to the operation requirement and sends the expected track to the main control board through the signal receiving and sending device;
step four: according to the vector relation, an inverse kinematics model of the parallel mechanical arm mechanism is established, and the end pose of the mechanical arm required by the current task point in the expected track of the end of the mechanical arm is converted into the virtual rod length between the equivalent rotating point on the motor shaft of the direct current servo motor 8 and the connecting point of the parallel mechanical arm movable platform 13;
step five: resolving the virtual rod length into an expected rotation angle of the direct current servo motor 8; in the fifth step, solutions of two expected rotation angles are obtained, and one is selected as a final expected rotation angle according to actual conditions;
step six: the parallel mechanical arm control module controls the corresponding direct current servo motor 8 to rotate to a desired rotation angle, and controls the actuating mechanism 15 to act. When the actuating mechanism 15 is an actuating paw, after the direct current servo motor 8 rotates to a desired rotation angle, the open-close state of the actuating paw at a set gripping point is controlled simultaneously in a gripping task, and when the actuating paw reaches a placing point, the actuating paw is opened, so that the operation is completed.
Further, in the first step, firstly, the inertial coordinate system is marked as { E }, the body coordinate system is marked as { B }, and the robot arm end coordinate system is marked as { C }, and then the coordinates of the quadrotor aircraft in the inertial coordinate system { E } are obtained according to the sensor module of the quadrotor aircraft and are expressed as P1＝[x1 y1 z1]TThe Euler angle is expressed as
Figure BDA0002555939110000111
The rotation matrix of the four-rotor aircraft under an inertial coordinate system is R1：
Figure BDA0002555939110000112
Wherein c represents cosine operation and s represents sine operation;
Figure BDA0002555939110000113
representing the roll angle, theta, of a four-rotor aircraft1Representing pitch angle of a quad-rotor aircraft，ψ1Representing the yaw angle of a four-rotor aircraft;
euler angle phi1Comprises the following steps:
Figure BDA0002555939110000114
acquiring the coordinate expression P of the tail end of the mechanical arm in an inertial coordinate system { E } according to the sensor module of the mechanical arm moving platform2＝[x2 y2 z2]TCalculating the rotation matrix R of the mechanical arm moving platform by the same method2。
The rotation matrix of the tail end of the parallel mechanical arm mechanism under the inertial coordinate system is R2；
Corresponding Euler angle phi2Comprises the following steps:
Figure BDA0002555939110000115
Figure BDA0002555939110000116
representing the roll angle, theta, of the end of the parallel robot arm mechanism2Indicating the pitch angle, psi, of the end of the parallel-connected robot arm mechanism2Indicating a yaw angle of the end of the parallel mechanical arm mechanism;
in step three, the planning of the expected trajectory of the end of the mechanical arm comprises:
in a track tracking working mode, the ground workstation generates an expected pose P of the tail end of the mechanical arm in an inertial coordinate system { E } at the current moment2dAnd phi2dThe whole time sequence is the expected track; under the point-to-point working mode, the ground station carries out cubic polynomial interpolation between the current pose and the target pose of the tail end of the mechanical arm to obtain the expected coordinate P of the tail end of the mechanical arm under an inertial coordinate system { E }2dAnd desired Euler angle phi2d；
The rotation matrix R of the desired trajectory2dComprises the following steps:
Figure BDA0002555939110000121
Figure BDA0002555939110000122
roll angle, θ, representing a desired trajectory of the end of the parallel-connected robotic arm mechanism2dPitch angle, psi, representing a desired trajectory of the end of the parallel robot2dA yaw angle representing a desired trajectory of the end of the parallel linkage mechanical arm mechanism;
and (3) calculating a coordinate P of the expected track point of the tail end of the mechanical arm in a body coordinate system { B }: p ═ P2d-P1(ii) a In the formula P1Representing the coordinates of the four-rotor aircraft in an inertial coordinate system; then the rotation matrix R of the expected track point at the end of the mechanical arm in the body coordinate system is:
Figure BDA0002555939110000123
and sending the rotation matrix R to a main control board through a signal receiving and sending device.
Further, as shown in fig. 4, in the fourth step of the present embodiment, the center of the cross 17 of the two-degree-of-freedom connecting mechanism 9 is moved to the corresponding motor shaft along the corresponding motor rocker arm 10 direction, so as to obtain the equivalent rotation point Bi(ii) a The six equivalent rotation points are in a common circle;
six equivalent rotation points BiDenoted b in the body coordinate systemi：
bi＝[rbcosδi rbsinδi h]T，
Wherein i is 1, 2, 3, … …, 6;
in the formula rbIs an equivalent rotation point BiDistance, delta, to the center of the circle in which the six equivalent points of rotation lieiIs an equivalent rotation point BiThe rotation angle corresponding to a connecting line of centers of circles where the six equivalent rotation points are located, and h is the distance between a plane where the six equivalent rotation points are located and an XOY plane of the body coordinate system;
similarly, six connecting points C on the parallel mechanical arm moving platform 13 are connectediAt the end of the arm coordinate systemIs represented by ci：
ci＝[rccosγi rcsinγi 0]T，
In the formula rcIs a connection point CiDistance, gamma, to the center of the circle in which the six points of connection lieiIs a connection point CiThe rotating angle corresponds to a connecting line of the centers of the circles where the six connecting points are located;
biand ciVectors that are all fixed parameters;
b is to beiAnd CiAfter connection to obtain
Figure BDA0002555939110000131
According to the vector relation, the vector relation is determined,
Figure BDA0002555939110000132
expressed as l in the body coordinate systemi：
li＝P+Rci-bi，(3)
By carrying out modulus taking operation on the formula (3), an inverse kinematics model of the parallel mechanical arm mechanism is established, the expected pose of the tail end of the mechanical arm is converted into the distance between an equivalent rotating point on a motor shaft and a connecting point of a movable platform, and the length | l of the virtual rod is obtainediI is:
Figure BDA0002555939110000133
the formula (4) reflects that the inverse kinematics model of the parallel mechanical arm has a unique solution and is convenient to solve, which is an advantage that the serial mechanical arm does not have.
In step five, the compound is treated with BiEstablishing a resolving coordinate system for the origin, wherein the coordinate axis direction of the resolving coordinate system is the same as that of the machine body coordinate system; b isiJiRepresenting a motor rocker arm 10, C of length piJiRepresenting a connecting rod 11, alpha, of length qiDesired angle of rotation, beta, of the motor to be solvediIs a rotation plane of the DC servo motor 8 and XB in resolving coordinatesiThe included angle formed by the Z plane is formed,is a fixed parameter;
FIG. 4 shows the relationship between the virtual rod length of the parallel mechanical arm, the triangular relationship between the motor rocker arm 10 and the connecting rod 11, and the center J of the cross 17 of the two-degree-of-freedom connecting mechanism 9iThe coordinates in the solved coordinate system are expressed as:
Figure BDA0002555939110000134
virtual rod length vector liThe three-axis components under the resolving coordinate system are respectively marked as lix、liy、lizAccording to the cosine theorem, the following results are obtained:
Figure BDA0002555939110000141
to simplify the expression, the following variable substitutions are made:
Figure BDA0002555939110000142
according to the auxiliary angle formula, the following results are obtained:
Figure BDA0002555939110000143
then solve for alphaiTo obtain two solutions alpha of the desired rotation anglei1And alphai2：
Figure BDA0002555939110000144
And selecting one solution closest to the current rotation angle of the DC servo motor 8 as the expected rotation angle.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims (3)

1. A method for calculating an expected rotation angle of a rotary parallel flying mechanical arm system is realized based on the rotary parallel flying mechanical arm system, the flying mechanical arm system comprises a four-rotor aircraft, a parallel mechanical arm mechanism, a centralized control module (3) and an actuating mechanism (15),
a centralized control module (3) is arranged in the center of the lower surface of the four-rotor aircraft; the head end of the parallel mechanical arm mechanism is connected with the four-rotor aircraft, and the tail end of the parallel mechanical arm mechanism is detachably connected with the executing mechanism (15);
the parallel mechanical arm mechanism has a six-degree-of-freedom rotatable structure and drives the actuating mechanism (15) to reach a task point at an expected pose;
the four-rotor aircraft comprises a propeller (1), a brushless motor (2), a horn (4) and a rotor aircraft chassis (5),
the four machine arms (4) are connected into a cross structure; a brushless motor (2) is fixed on the upper surface of the tail end of each machine arm (4), and a propeller (1) is installed on an output shaft of each brushless motor (2); four arms (4) connected by a cross structure are fixed on the upper surface of a rotorcraft chassis (5) in the middle; a centralized control module (3) is arranged at the center of the lower surface of the gyroplane chassis (5); the gyroplane chassis (5) is of a regular hexagon structure;
the parallel mechanical arm mechanism comprises a support column (6), a parallel mechanical arm fixed platform (7), a direct current servo motor (8), a two-degree-of-freedom connecting mechanism (9), a motor rocker arm (10), a connecting rod (11), a three-degree-of-freedom connecting mechanism (12) and a parallel mechanical arm moving platform (13),
the parallel mechanical arm fixed platform (7) is of a regular hexagon structure, has the same size with the gyroplane chassis (5), and is coaxially arranged; the parallel mechanical arm fixed platform (7) is connected with the gyroplane chassis (5) through six uniformly distributed support columns (6);
the parallel mechanical arm fixed platform (7) is provided with a direct current servo motor (8) corresponding to each side, and the rotating plane of each direct current servo motor (8) is vertical to the corresponding side of the parallel mechanical arm fixed platform (7); the output shaft of each direct current servo motor (8) is sleeved in the protruding end of one motor rocker arm (10), the tail end of the motor rocker arm (10) is connected with the head end of one connecting rod (11) through a two-degree-of-freedom connecting mechanism (9), and the tail end of each connecting rod (11) is connected with a parallel mechanical arm moving platform (13) through a three-degree-of-freedom connecting mechanism (12); the six three-degree-of-freedom connecting mechanisms (12) are in a same circle with the connecting points of the parallel mechanical arm moving platform (13);
a notch is formed in the position, corresponding to each side, of the parallel mechanical arm fixed platform (7), and each motor rocker arm (10) drives the corresponding two-degree-of-freedom connecting mechanism (9) to penetrate through one notch under the driving of a direct-current servo motor (8), so that an actuating mechanism (15) is driven to change the pose;
the notch comprises a rectangular notch; each rectangular notch is vertical to the corresponding side of the parallel mechanical arm fixed platform (7);
the direct current servo motor (8) is positioned in an included angle between the corresponding side of the parallel mechanical arm fixed platform (7) and the long side of the rectangular notch and is close to the edge of the corresponding side of the parallel mechanical arm fixed platform (7);
the adjacent rectangular gaps are overlapped after the parallel mechanical arm fixed platform (7) rotates for 60 degrees;
the two-degree-of-freedom connecting mechanism (9) and the three-degree-of-freedom connecting mechanism (12) have the same structure and respectively comprise a male hinge (16), a cross shaft (17) and a female hinge (18); one shaft of the cross shaft (17) is rotationally connected with the male hinge (16), and the other shaft of the cross shaft (17) is rotationally connected with the female hinge (18);
in the two-degree-of-freedom connecting mechanism (9), a male hinge (16) is fixed in a concave hole at the tail end of a motor rocker arm (10), so that the male hinge (16) cannot rotate; the female hinge (18) is connected with the head end of the connecting rod (11);
in the three-degree-of-freedom connecting mechanism (12), a female hinge (18) is connected with the tail end of a connecting rod (11), and a male hinge (16) is arranged in a through hole correspondingly arranged on a parallel mechanical arm moving platform (13) and is rotationally connected with the parallel mechanical arm moving platform (13);
the centralized control module (3) comprises a gyroplane integrated module and a parallel mechanical arm control module;
the gyroplane integration module comprises a power supply module, a sensor module and a flight controller module, wherein the power supply module is used for providing working power supply for the four-rotor aircraft, the sensor module is used for acquiring the motion state of the four-rotor aircraft in real time, and the flight controller module is used for controlling the four-rotor aircraft to run according to aircraft control signals or an expected track of the aircraft;
the parallel mechanical arm control module comprises a power supply, a main control board and a signal transceiving device, wherein the power supply is used for providing a working power supply for the parallel mechanical arm mechanism, the main control board is used for controlling the pose of the tail end of the parallel mechanical arm mechanism according to a mechanical arm control signal or an expected track of the tail end of the mechanical arm, and the main control board is interacted with the ground station through the signal transceiving device;
the parallel mechanical arm mechanism also comprises a tail end sensor module, wherein the tail end sensor module is fixed at the center of the parallel mechanical arm moving platform (13) and is used for acquiring the current motion state of the tail end of the parallel mechanical arm mechanism in real time;
the actuator (15) comprises an actuator gripper or an aerial camera;
when the executing mechanism (15) is an executing paw, the executing paw is driven by the steering engine (14);
the calculating method is characterized by comprising the following steps:
the method comprises the following steps: acquiring the motion state of the four-rotor aircraft and the current motion state of the tail end of the parallel mechanical arm mechanism, and calculating to obtain a rotation matrix of the four-rotor aircraft;
step two: the flight controller module controls the four-rotor aircraft to reach a preset range of a task point according to the current motion state;
step three: the ground station plans the expected track of the tail end of the mechanical arm according to the operation requirement and sends the expected track to the main control board through the signal receiving and sending device;
step four: according to the vector relation, an inverse kinematics model of the parallel mechanical arm mechanism is established, and the end pose of the mechanical arm required by the current task point in the expected track of the end of the mechanical arm is converted into the virtual rod length between the equivalent rotating point on the motor shaft of the direct current servo motor (8) and the connecting point of the parallel mechanical arm movable platform (13);
step five: resolving the virtual rod length into an expected rotation angle of a direct current servo motor (8);
step six: the parallel mechanical arm control module controls the corresponding direct current servo motor (8) to rotate to an expected rotation angle, and simultaneously controls the actuating mechanism (15) to act.
2. The method for calculating the expected rotation angle of a rotary parallel-type flying robot system according to claim 1,
in the first step, the rotation matrix of the four-rotor aircraft in the inertial coordinate system is R1：
Figure FDA0003018625810000031
Wherein c represents cosine operation and s represents sine operation;
Figure FDA0003018625810000032
representing the roll angle, theta, of a four-rotor aircraft1Representing the pitch angle, psi, of a four-rotor aircraft1Representing the yaw angle of a four-rotor aircraft;
euler angle phi1Comprises the following steps:
Figure FDA0003018625810000033
the rotation matrix of the tail end of the parallel mechanical arm mechanism under the inertial coordinate system is R2；
Rotation matrix R2Is calculated and the rotation matrix R1The calculation methods are the same;
corresponding Euler angle phi2Comprises the following steps:
Figure FDA0003018625810000034
Figure FDA0003018625810000037
representing the roll angle, theta, of the end of the parallel robot arm mechanism2Indicating the pitch angle, psi, of the end of the parallel-connected robot arm mechanism2Indicating a yaw angle of the end of the parallel mechanical arm mechanism;
in step three, the planning of the expected trajectory of the end of the mechanical arm comprises:
under the point-to-point working mode, the ground station carries out cubic polynomial interpolation between the current pose and the target pose of the tail end of the mechanical arm to obtain the expected coordinate P of the tail end of the mechanical arm under an inertial coordinate system2dAnd desired Euler angle phi2d；
The rotation matrix R of the desired trajectory2dComprises the following steps:
Figure FDA0003018625810000035
Figure FDA0003018625810000036
roll angle, θ, representing a desired trajectory of the end of the parallel-connected robotic arm mechanism2dPitch angle, psi, representing a desired trajectory of the end of the parallel robot2dA yaw angle representing a desired trajectory of the end of the parallel linkage mechanical arm mechanism;
calculating the coordinate P of the expected track point at the tail end of the mechanical arm in a machine body coordinate system: p ═ P2d-P1(ii) a In the formula P1Representing the coordinates of the four-rotor aircraft in an inertial coordinate system; then the rotation matrix R of the expected track point at the end of the mechanical arm in the body coordinate system is:
Figure FDA0003018625810000041
and sending the rotation matrix R to a main control board through a signal receiving and sending device.
3. The method for calculating the expected rotation angle of a rotary parallel-type flying robot system according to claim 2,
in the fourth step, the center of a cross shaft (17) of the two-degree-of-freedom connecting mechanism (9) is moved to the corresponding motor shaft along the direction of the corresponding motor rocker arm (10) to obtain an equivalent rotating point Bi(ii) a The six equivalent rotation points are in a common circle;
six equivalent rotation points BiDenoted b in the body coordinate systemi：
bi＝[rbcosδi rbsinδi h]T，
Wherein i is 1, 2, 3, … …, 6;
in the formula rbIs an equivalent rotation point BiDistance, delta, to the center of the circle in which the six equivalent points of rotation lieiIs an equivalent rotation point BiThe rotation angle corresponding to a connecting line of centers of circles where the six equivalent rotation points are located, and h is the distance between a plane where the six equivalent rotation points are located and an XOY plane of the body coordinate system;
similarly, six connecting points C on the parallel mechanical arm moving platform (13)iDenoted c in the robot arm end coordinate systemi：
ci＝[rccosγi rcsinγi 0]T，
In the formula rcIs a connection point CiDistance, gamma, to the center of the circle in which the six points of connection lieiIs a connection point CiThe rotating angle corresponds to a connecting line of the centers of the circles where the six connecting points are located;
b is to beiAnd CiAfter connection to obtain
Figure FDA0003018625810000042
Expressed as l in the body coordinate systemi：
li＝P+Rci-bi， (3)
By performing a modulo operation on equation (3), a set-up is madeInverse kinematics model of the parallel manipulator mechanism, then the virtual rod length | liI is:
Figure FDA0003018625810000051
in step five, the compound is treated with BiEstablishing a resolving coordinate system for the origin, wherein the coordinate axis direction of the resolving coordinate system is the same as that of the machine body coordinate system; b isiJiRepresents a motor rocker arm (10), C, of length piJiRepresenting a connecting rod (11) of length q, alphaiDesired angle of rotation, beta, of the motor to be solvediIs a rotation plane of the DC servo motor (8) and XB in resolving coordinatesiThe included angle formed by the Z plane is formed,
the center J of a cross shaft (17) of the two-degree-of-freedom connection mechanism (9)iThe coordinates in the solved coordinate system are expressed as:
Figure FDA0003018625810000052
virtual rod length vector liThe three-axis components under the resolving coordinate system are respectively marked as lix、liy、lizAccording to the cosine theorem, the following results are obtained:
Figure FDA0003018625810000053
to simplify the expression, the following variable substitutions are made:
Figure FDA0003018625810000054
according to the auxiliary angle formula, the following results are obtained:
Figure FDA0003018625810000055
then solve for alphaiTo obtain two solutions alpha of the desired rotation anglei1And alphai2：
Figure FDA0003018625810000056
And selecting one solution closest to the current rotation angle of the DC servo motor (8) as the expected rotation angle.
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