CN111216129B - Active-passive combined series-parallel force feedback equipment gravity compensation method - Google Patents

Active-passive combined series-parallel force feedback equipment gravity compensation method Download PDF

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CN111216129B
CN111216129B CN202010013114.5A CN202010013114A CN111216129B CN 111216129 B CN111216129 B CN 111216129B CN 202010013114 A CN202010013114 A CN 202010013114A CN 111216129 B CN111216129 B CN 111216129B
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CN111216129A (en
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李静蓉
符俊岭
谢海龙
王清辉
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South China University of Technology SCUT
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Abstract

The invention discloses an active and passive combined series-parallel force feedback equipment gravity compensation method, which comprises the following steps: step 1, calculating the torque tau consumed by each driving motor when realizing active gravity compensation based on motor torque A (ii) a Step 2, calculating the torque tau generated by the passive compensation structure of the passive extension spring to the branch chain S (ii) a Step 3, the active gravity compensation torque tau obtained in the step 1 A And the torque tau generated by the spring passive compensation structure on the branch chain S Calculating the torque tau actually required by each motor to realize gravity compensation of the force feedback equipment under the space attitude; and 4, calculating and compensating the current I required to be output by each motor when the force feedback equipment is kept balanced under the attitude, and realizing the gravity balance of the force feedback equipment at the position. The invention provides an active and passive combined gravity compensation method suitable for series-parallel force feedback equipment, which improves the immersion sense of a user in the interaction process of operating the force feedback equipment and improves the output force of the equipment in a motion space under the condition of not increasing the rated torque of a motor.

Description

Active and passive combined series-parallel force feedback equipment gravity compensation method
Technical Field
The invention relates to the technical field of force/touch interaction in the field of virtual reality, in particular to an active and passive combined gravity compensation method for a series-parallel force feedback device.
Background
As a novel man-machine interaction way, the force feedback/touch interaction technology is widely applied to the fields of virtual assembly, product design, manufacturing simulation virtual operation training and the like. When a user operates the force feedback equipment, the gravity of the self mechanism of the equipment can influence the perception of the reality of the feedback force of the virtual environment, if the gravity of the equipment is not compensated, the user feels the resultant force of the self gravity of the equipment and the feedback force of the virtual environment, which obviously does not meet the purpose of force sense interaction; secondly, the user may feel tired in the muscles by operating the force feedback device for a long time, reducing the operation immersion. Therefore, it is necessary to compensate for the gravitational force caused by the equipment linkage. The goals of gravity compensation are: the force feedback device is kept balanced in any posture of the motion space without the action of external force applied by a user.
In recent years, a great deal of literature has conducted gravity compensation research on the proposed force feedback devices, and the gravity compensation is mainly divided into two modes of active compensation and passive compensation. The active compensation is realized by balancing the gravity of the equipment through the output reverse force/moment of the motor, and the active compensation has the advantages that an additional mechanism is not needed, the complexity and the space size of the mechanism are not increased, but a large amount of torque of the motor is consumed, and particularly when the gravity of the equipment is large, the output force performance of the force feedback equipment is influenced; passive compensation, through adding the balancing weight or the gravity of the spring balancing equipment, the method does not need the motor to consume extra torque, is proved to be an effective method for balancing the gravity of the mechanism, but the method introduces the structures of the balancing weight, the auxiliary connecting rod and the like, can cause interference between the mechanisms during movement, and is not suitable for complex parallel mechanisms.
Patent CN 102320040B provides a force feedback interaction device capable of automatically adjusting self-weight balance, and a direct current motor is innovatively adopted to control a balance slide block to automatically compensate self-weight of an equipment arm mechanism in real time, so that hand fatigue is reduced. However, this method requires the introduction of a motor, a speed reducing mechanism, a balance weight, a balance lever, etc., which increases the inertia of the device during movement.
Patent CN 102825601B provides an anthropomorphic 6-degree-of-freedom robot gravity balance method, three joints of a wrist type adopt a symmetrical design and a counterweight design, so that a mass center of the structure is intersected with a small arm rod piece at one point, and gravity compensation of a position mechanism is realized based on a counterweight and electric drive torque. The method is suitable for gravity compensation of a series mechanism and is not suitable for a parallel mechanism with a complex structure.
Patent CN105550466A proposes an optimal spring gravity compensation method for a force feedback device, which adopts two springs to compensate gravity of a series force feedback device, and considers the influence of factors such as stiffness coefficient, installation position, and length of the springs, but this method cannot realize complete gravity compensation of the force feedback device.
Patent CN107738275A proposes a cam tension spring mechanism for gravity compensation of a mechanical arm, which converts the gravitational potential energy of the mechanical arm into elastic potential energy by adding a disk cam and a tension spring unit, so as to achieve the effect of complete gravity balance of the mechanical arm in an effective working space. However, this method is only suitable for a simple structure with a single degree of freedom, and is not suitable for a force feedback device with multiple degrees of freedom, especially parallel connection.
Mashayekhi et al (VirSense: a novel vertical device with fixed-base motors and a gravity compensation system [ J ]) for a six-degree-of-freedom tandem haptic device, two springs were used to compensate for 95% of the link weight, and the other 5% of the weight was achieved based on motor active compensation. However, the proposed gravity compensation method has no versatility, and requires the introduction of a very complicated and specially designed pulley transmission system.
Simion scientific I (Static balancing with elastic systems of Delta parallel robots [ J ]) researches a Static balance method of a Delta parallel mechanism which is vertically placed, and each branch chain is added with 3 springs and two connecting rods to realize the Static balance of the mechanism in a motion space. However, the method is complex in structure, difficult to process and not adopted in practical application.
The elevation J (Haptic Device Using a New Device heavy Parallel Mechanism [ J ]) carries out gravity compensation research on the designed Delta-R Redundant force feedback equipment, 50% of gravity is compensated by adding a balancing weight, and the rest gravity is compensated based on motor torque. However, the introduction of the weight block increases the inertia of the force feedback device during movement, and is not suitable for the horizontally placed force feedback device due to the limitation of the spatial position of the mechanism.
Dehkoridi M (modeling and Experimental Evaluation of a Static Balancing Technique for a New horizontal Parallel Mounted 3-UPU Parallel Mechanism [ J ]) performed a gravity compensation study on a Horizontally placed three-degree-of-freedom Parallel force feedback device, with passive gravity compensation by adding 3 springs. This approach still requires the motor to output torque to achieve balance of the force feedback device and the three springs introduce unwanted force and the motor needs to output opposing forces to balance the force generated by the springs.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an active and passive combined series-parallel force feedback equipment gravity compensation method. The method aims at the horizontally arranged parallel-series type force feedback equipment, accurate gravity compensation is achieved through an active compensation method based on motor torque, and the force feedback equipment is static at any point in a motion space. According to the characteristics of torque consumption of three motors during active gravity compensation, a spring is introduced into a branched chain with the maximum torque consumption for passive compensation, the torque value consumed by gravity compensation is reduced, and the available torque of a force feedback device for feeding back output force is increased. The method of active gravity compensation based on motor torque and passive gravity compensation based on the spring passive compensation structure is combined, so that the series-parallel force feedback equipment can be static at any point in a motion space, complete gravity compensation is realized, and the immersion sense of a user when operating the force feedback equipment is improved.
The invention is realized by at least one of the following technical schemes.
An active-passive combined series-parallel force feedback equipment gravity compensation method comprises the following steps:
step 1, calculating the torque tau consumed by each driving motor when realizing active gravity compensation based on motor torque according to statics of a parallel mechanism of force feedback equipment A ；
Step 2, according to the torque consumed by each joint motor during active gravity compensation of the force feedback equipment, introducing a spring passive compensation structure into the uppermost branch chain of the parallel mechanism, optimizing the parameters such as the spring installation position, stiffness coefficient and the like of the spring passive compensation structure, and according to a passive compensation torque formula, calculating the torque tau generated by the passive compensation structure of the passive extension spring on the branch chain where the passive extension spring is located S ；
Step 3, the active gravity compensation torque tau obtained in the step 1 A And the torque tau generated by the spring passive compensation structure on the branched chain S Calculating the torque tau actually required by the motors to realize gravity compensation of the force feedback equipment under the space attitude;
and 4, calculating and compensating the current I required to be output by each motor when the force feedback equipment is kept balanced under the attitude by using the motor output torque tau obtained in the step 3, and realizing the gravity balance of the force feedback equipment at the position.
Further, the series-parallel force feedback device comprises a three-degree-of-freedom parallel mechanism and a series rotating mechanism, and the series rotating mechanism is fixed at the central position of the parallel mechanism moving platform.
Further, in the step 1, the quality of the mechanism and the connecting rod of the series-parallel force feedback device is simplified according to a statics analysis method, and the method specifically comprises the following steps:
1) Simplifying the serial mechanism into mass points acting on the center of the parallel mechanism motion platform;
2) Part of the mass of the second rod piece of each branched chain of the parallel mechanism is attached to the center of the motion platform, and part of the mass is attached to the joint where the first rod piece of each branched chain is connected with the second rod piece;
3) And the second rod piece of each branched chain of the parallel mechanism of the force feedback equipment is equivalent to a two-force rod.
Further, step 1 calculates the torque τ consumed by each driving motor when realizing active gravity compensation based on the motor torque A The method comprises the following steps:
(1) Firstly, carrying out stress balance analysis on a motion platform of the parallel mechanism to obtain the internal force f of a second rod piece in three branched chains i ；
(2) Calculating the acting force f of the second rod on the first rod i The torque generated at the rotating joint of the motor, the torque generated by the gravity of the first rod piece and the torque generated by the gravity of the second rod piece attached to the first rod piece;
(3) The sum of the three torques obtained in step (2) is the active gravity compensation torque tau A 。
Further, the passive compensation in step 2 is realized by adding a spring passive compensation structure to the uppermost branch chain of the parallel mechanism of the force feedback device.
Furthermore, the added spring passive compensation structure comprises a first spring fixing piece, a second spring fixing piece, a steel wire rope, an extension spring, a winding pulley and a pulley fixing piece; one end of the extension spring and the steel wireThe wire rope is wound by a winding pulley arranged on the pulley fixing piece for one circle, the wire rope is fixedly locked by a nut of a first spring fixing piece arranged on a first rod piece of the branched chain of the parallel mechanism, and the other end of the spring is fixed in front of the fixed base by a second spring fixing piece; the branched chain drives the spring to stretch when rotating, acts on the first rod piece, and generates spring torque tau S The concrete formula is as follows:
τ S ＝FL＝K 1 L x L AS sin(α 0 +α 1 )
wherein the content of the first and second substances,
Figure BDA0002357866770000041
L VS 2 ＝h 0 2 +L AS 2 -2h 0 L AS cos(90°-θ i )
Figure BDA0002357866770000042
Figure BDA0002357866770000043
K 1 is the spring stiffness coefficient, L x For spring extension, L AS Is spring attachment point distance A i S is the connection point of the spring and the first rod of the branched chain of the parallel mechanism, h 0 For the installation height of the winding pulley and the radius r of the winding pulley 0 Length L of the first rod 1 The equivalent length L of the second rod 2 ，θ i (i =1,2, 3) is an angle between the first rod of the parallel mechanism and the horizontal direction of the force feedback device, namely an angle between the first rod and the Z-axis direction.
Further, the optimization of step 2 is specifically the stiffness coefficient K of the spring 1 Pulley mounting height h 0 The position of the spring at the first link fixing point S is optimized, and the optimization comprises the following steps:
s1, setting a motion track of the force feedback equipment along a Z-axis of a motion space, wherein the motion track isMoving the base to the maximum position of the Z-axis coordinate from the position close to the fixed base; obtaining the torque consumed by the driving of the three motors during the active gravity compensation according to the step 1, and obtaining the torque difference value of the first motor, the second motor and the third motor along with the joint angle theta due to the symmetrical distribution of the second motor and the third motor i Curve of change, which is taken as target torque tau required to be generated by the spring P ；
s2 actual torque τ generated for the spring S With target torque τ P Is integrated to calculate the average torque error tau of the angle change process E ；
s3, mixing tau E The minimum value of the coefficient K is used as an objective function for optimizing the parameters of the spring passive compensation structural part to obtain the stiffness coefficient K 1 Pulley mounting height h 0 The numerical value of the fixed point S is as follows:
Figure BDA0002357866770000051
wherein, theta n+1 Is the maximum value of the rotation angle, tau, of the first connecting rod of the branched chain of the parallel mechanism S (θ) is the torque actually generated by the spring structure, τ P (θ) is the target torque that the spring structure needs to produce.
Further, the actually required torque τ of the motor in step 3 is the torque τ compensated by active gravity A With passive compensation torque tau produced by the spring S The difference of (a) is obtained, the formula is as follows:
τ＝[τ A1 -τ S ,τ A2 ,τ A3 ]
wherein, tau A1 ,τ A2 ,τ A3 Respectively representing the torque, tau, required to be generated by the three motors based on the active gravity compensation in step 1 S And (3) showing the spring torque generated by the passive spring passive compensation structure on the uppermost branched chain in the step 2.
Further, the motor current I in step 4 is the torque τ actually required to be output by the motor and the motor torque constant K M Obtaining the relation of (A), obtaining the motor current IEach branched chain motor of the force feedback equipment outputs current, so that the force feedback is arranged at a spatial position and can keep balance, and the formula is as follows:
Figure BDA0002357866770000052
wherein, tau is the torque which is actually required to be output by the motor, and the torque constant of the motor.
Compared with the prior art, the invention has the advantages and effects that:
1) The invention adopts a method of combining the motor torque active gravity compensation and the spring passive compensation structure passive gravity compensation to realize the complete gravity compensation of the horizontally placed series-parallel force feedback equipment. The user does not need to exert extra force, and the equipment can keep still at any point in the motion space, has improved the sense of immersion that the feedback equipment carries out the interactive operation process when the user uses.
2) When the horizontally arranged parallel-series force feedback equipment is used for gravity compensation, the torque difference consumed by the uppermost motor is large. A spring passive compensation structure is introduced into a branched chain with the largest motor consumption torque, so that the torque difference consumed by three motors is reduced, the available torque of the branched chain motor for outputting force is increased, and the integral output force of the force feedback equipment is increased.
3) The passive gravity compensation device adopts the spring passive compensation structure for passive gravity compensation, compared with a mode of adding a balancing weight, the spring has the advantages of light weight, small volume and the like, and the inertia of the device cannot be increased by the added spring passive compensation structure. Compared with the passive gravity compensation method by adding a plurality of auxiliary connecting rods, the spring passive compensation structure has the advantages of simple structure, no motion interference, no increase of equipment volume and the like.
Drawings
FIG. 1 is a schematic diagram of a series-parallel force feedback device and a structure diagram of a spring passive compensation in the present embodiment;
FIG. 2 is a schematic diagram illustrating the gravity distribution of the second rod of the parallel mechanism of the series-parallel type force feedback device of the present embodiment;
FIG. 3 is a schematic diagram of the simplified structure of the series-parallel force feedback device and the equivalent effect of gravity in the series structure;
FIG. 4 is a schematic diagram of force analysis of a motion platform of a parallel mechanism of the series-parallel force feedback device of the present example;
FIG. 5 is a schematic diagram of a force analysis of a single branched chain of a parallel mechanism of the series-parallel type force feedback device of the present embodiment;
FIG. 6 is a schematic diagram of the passive compensation structure of the spring of the present embodiment;
the system comprises a parallel mechanism with 1-three degrees of freedom, a fixed base of the parallel mechanism 11, a first rod piece of each branched chain of the parallel mechanism 12, a second rod piece of each branched chain of the parallel mechanism 13 and a moving platform of the parallel mechanism 14; 2-a serial rotating mechanism; 31-extension spring, 32-winding pulley fixing piece, 33-steel wire rope, 34-winding pulley, 35-first spring fixing piece and 36-second spring fixing piece.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings and examples, but the scope of the invention is not limited thereto.
As shown in fig. 1, a method for gravity compensation of an active-passive combined series-parallel force feedback device includes the following steps:
step 1, calculating the torque tau consumed by each driving motor when realizing active gravity compensation based on motor torque according to statics of a parallel mechanism of force feedback equipment A 。
Specifically, the force feedback device in this example is a series-parallel force feedback device, as shown in fig. 1, including a parallel mechanism 1 with three degrees of freedom and a series rotating mechanism 2, where the series rotating mechanism 2 is fixed at a central position of a moving platform 14 of the parallel mechanism 1. Rotation angle theta of three branched chain first rod pieces 12 of force feedback parallel mechanism 1 i (i =1,2,3) is read by an encoder, in this example an MR228456 model encoder, manufactured by Maxon corporation, with an angular resolution of 0.36 ° and a maximum frequency of 200KHZ. In the present example, the range of the rotation angle of each branch chain of the parallel mechanism of the force feedback device is limited to [ 27-120 DEG ]]；
When static analysis is performed, the mass of the serial rotating mechanism 2 and the second connecting rod 13 of the parallel mechanism 1 of the force feedback device shown in fig. 1 is simplified, specifically as follows:
1) As shown in fig. 2 and 3, the gravity of the series mechanism 2 is simplified into a mass point O acting on the center of the parallel mechanism moving platform 14 and having a mass G String ；
2) As shown in FIG. 2, in this example, the masses G of the branched second bars 12 of the parallel mechanism 1 P The mass added to the center of the motion platform 14 is G P1 The mass at the joint where the first rod 12 and the second rod 13 of each additional branch are connected is G P2 Mass of the parallel motion platform is G M ；
3) The second rod 13 of each branch of the parallel mechanism 1 of the force feedback device is equivalent to a two-force rod.
In step 1, calculating the torque tau consumed by each driving motor when realizing active gravity compensation based on motor torque A The method comprises the following steps:
1) Firstly, the force balance analysis is carried out on the moving platform 14 of the parallel mechanism 1 of the force feedback equipment, the force analysis schematic diagram of the moving platform is shown in fig. 4, and the internal force f of the second rod piece 13 in the three branched chains is obtained i The formula is as follows:
Figure BDA0002357866770000071
wherein the content of the first and second substances,
Figure BDA0002357866770000072
Figure BDA0002357866770000073
wherein P (x, y, z) is the center coordinate of the motion platform of the force feedback equipment, and is obtained by the positive kinematics formula of the parallel mechanism of the force feedback equipment, R is the radius of the motion platform, R is the radius of the fixed base, and L 1 Is the first link length, L 2 To be equivalent to the second link length, θ i (i =1,2, 3) is the angle between the first rod 12 of each branch of the parallel mechanism and the Z-axis direction, η i The included angle of each branched chain of the force feedback equipment,
Figure BDA0002357866770000074
as shown in FIG. 5, B i Is the connection point of the first connecting rod and the fixed base, C i I represents the ith branched chain of the parallel mechanism, and is the connection point of the first connecting rod and the second connecting rod.
2) As shown in FIG. 5, the force f of the second pin 13 on the first pin 12 is calculated i Torque generated at the motor rotary joint, f i The component force in the plane of the first bar 12 is
Figure BDA00023578667700000711
The gravity of the first pin 12 is G A ,G A The component force in the plane of the first bar 12 is
Figure BDA0002357866770000075
The gravity of the second pin 13 attached to the first pin 12 is G P2 ,G P2 The component force in the plane of the first bar 12 is
Figure BDA0002357866770000076
3)
Figure BDA00023578667700000712
，
Figure BDA0002357866770000077
Three forces in the active joint A i The torque generated is the motor torque consumed during the active gravity compensation, and the formula is used
Figure BDA0002357866770000078
Obtaining;
wherein tau is the torque which needs to be output by each branched-chain motor during active gravity compensation,
Figure BDA0002357866770000079
in the form of a vector representation of the length of the first link,
Figure BDA00023578667700000710
is a distance A from the centroid position of the first pin 12 i Vector representation of point distances.
And 2, introducing a spring to perform passive compensation on the first rod 12 of the uppermost branched chain of the parallel mechanism according to the torque consumed by each joint motor during the active gravity compensation of the force feedback equipment. According to a passive compensation torque formula, calculating the torque tau generated by the passive compensation structure of the passive extension spring to the branch chain where the passive extension spring is located S (ii) a In this example, as shown in fig. 1, a spring passive compensation structure is added to the branched first rod 12 at the top of the parallel mechanism, and the spring passive compensation structure includes an extension spring 31, a pulley fixing member 32, a steel wire 33, a winding pulley 34, a first spring fixing member 35, and a second spring fixing member 36. One end of the spring 31 is connected with a wire rope 33, the wire rope 33 winds around a winding pulley 34 for one circle, the wire rope 33 is fixedly locked through a first spring fixing piece 35, namely a nut, installed at the first rod piece 12 of the branched chain of the parallel mechanism, and the other end of the spring 31 is fixed in front of the fixing base 11 of the parallel mechanism through a second spring fixing piece 36. When the branched chain rotates, the spring 31 is driven to stretch and contract and acts on the first rod 12 to generate a spring torque tau S ；
As shown in fig. 6, the torque τ generated by the added passive tension spring passive compensation structure on the branch chain is calculated S The formula is as follows: tau is S ＝FL＝K 1 L x L AS sin(α 0 +α 1 )
Wherein the content of the first and second substances,
Figure BDA0002357866770000081
L VS 2 ＝h 0 2 +L AS 2 -2h 0 L AS cos(90°-θ i )
Figure BDA0002357866770000082
Figure BDA0002357866770000083
K 1 is the spring stiffness coefficient, L x For spring extension, L AS Is spring connection point distance A i S is the connection point of the spring and the first rod 12 of the branched chain of the parallel mechanism, h 0 For the installation height of the winding pulley and the radius r of the winding pulley 0 The length L of the first bar member 12 1 The second bar 13 has an equivalent length L 2 V is the center of the winding pulley;
step 2, optimizing the passive compensation structure of the spring is to optimize the stiffness coefficient K of the spring 1 Pulley mounting height h 0 The position of the spring at the first connecting rod fixing point S is optimized, and the method specifically comprises the following steps:
1) And setting a motion track of the force feedback equipment along the Z-axis of the motion space, and moving the force feedback equipment to the maximum position of the Z-axis coordinate from the position close to the fixed base. According to the step 1, the torques consumed by the three motors during the active gravity compensation are obtained, and the torque difference values consumed by the first motor, the second motor and the third motor along with the joint angle theta can be obtained due to the symmetrical distribution of the second motor and the third motor i Curve of change, which is taken as target torque tau required to be generated by the spring P ；
2) Torque tau actually generated for spring S With target torque τ P Is integrated, and the average torque error tau in the angle change process is calculated E Will tau be E Is used as an objective function for optimizing the spring mechanism parameters, and the formula is as follows:
Figure BDA0002357866770000091
wherein, theta n+1 Is the maximum value of the rotation angle, tau, of the first connecting rod of the branched chain of the parallel mechanism S (theta) is the torque actually generated by the spring structure, τ P (θ) target torque to be generated for the spring structure
In this example, a particle swarm optimization algorithm is adopted to optimize the parameters, K 1 Has an initial constraint range of 0.1 to 0.5](N/mm),L AS ConstrainingIn the range of [30 to 100%](mm),h 0 The constraint range is [0,60 ]](mm); the numerical value result obtained by optimization is used as the part processing parameter of the passive compensation structure of the spring in the example, and the torque tau generated by the passive compensation structure of the passive extension spring to the branch chain at the passive extension spring is further obtained S 。
Step 3, obtaining the active gravity compensation torque tau in the steps 1 and 2 A And the tension spring passively compensates the torque tau generated by the structure on the branch chain S Obtaining the torque tau actually required by the motors to realize gravity compensation of the force feedback equipment under the space attitude, and actually obtaining the torque tau according to the following formula:
τ＝[τ A1 -τ S ,τ A2 ,τ A3 ]
wherein, tau A1 ,τ A2 ,τ A3 Respectively representing the torque, tau, required to be generated by the three motors based on the active gravity compensation in step 1 S And (3) showing the spring torque generated by the passive spring passive compensation structure on the uppermost branched chain in the step 2.
Step 4, obtaining the output torque τ of the motor obtained in the step 3, in this embodiment, obtaining the current I required to be output by each motor when the force feedback device keeps balance under the attitude, where the formula is as follows:
Figure BDA0002357866770000092
wherein, tau is the torque actually needed to be output by the motor, and the motor torque constant K M In this example, the RE30 DC servo motor of Maxon, K M The value of (A) was 25.9mNm.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. The gravity compensation method of the active-passive combined series-parallel force feedback equipment is characterized in that the series-parallel force feedback equipment comprises a three-degree-of-freedom parallel mechanism and a series rotating mechanism; the parallel mechanism comprises a fixed base of the parallel mechanism, a first rod piece of each branched chain of the parallel mechanism, a second rod piece of each branched chain of the parallel mechanism and a moving platform of the parallel mechanism to form three branched chains; the serial rotating mechanism is fixed at the central position of a moving platform of the parallel mechanism;
the method comprises the following steps:
step 1, calculating the torque tau consumed by each driving motor when the driving motor torque is used for realizing active gravity compensation according to statics of a parallel mechanism of force feedback equipment A ；
Step 2, according to the torque consumed by each driving motor during active gravity compensation of the force feedback equipment, introducing a spring passive compensation structure into the uppermost branched chain of the parallel mechanism, optimizing the relevant parameters of the spring passive compensation structure, and according to a passive compensation torque formula, calculating the torque tau generated by the spring passive compensation structure on the branched chain where the spring passive compensation structure is located S ；
Step 3, the torque tau consumed by each driving motor during the active gravity compensation obtained in the step 1 A And the torque tau generated by the passive compensation structure of the spring on the branch chain S Calculating the torque tau actually required by each driving motor to realize gravity compensation of the force feedback equipment under the corresponding space attitude;
step 4, torque tau actually required by gravity compensation of the force feedback equipment is achieved by the driving motors obtained in the step 3 under the corresponding space postures, current I required to be output by the driving motors when the force feedback equipment keeps balance under the space postures is calculated and compensated, and gravity balance of the force feedback equipment under the space postures is achieved;
the added spring passive compensation structure comprises a first spring fixing piece, a second spring fixing piece, a steel wire rope, an extension spring, a winding pulley and a pulley fixing piece; one end of an extension spring is connected with a steel wire rope, the steel wire rope winds a winding pulley arranged on a pulley fixing piece for a circle, the steel wire rope is fixedly locked through a nut of a first spring fixing piece arranged at a first rod piece of a branched chain of the parallel mechanism, and the other end of the extension spring is fixed in front of the fixing base through a second spring fixing piece; the branch chain drives the extension spring to extend and contract when rotatingActing on the first rod to generate a torque tau generated by the passive compensation structure of the spring to the branch chain S The concrete formula is as follows:
τ S ＝FL＝K 1 L x L AS sin(α 0 +α 1 )；
wherein the content of the first and second substances,
Figure FDA0004052225460000011
L VS 2 ＝h 0 2 +L AS 2 -2h 0 L AS cos(90°-θ)；
Figure FDA0004052225460000012
Figure FDA0004052225460000013
K 1 is the spring stiffness coefficient, L x The elongation of the tension spring is shown as S, which is a connection point of the steel wire rope and a first rod piece of a branched chain of the parallel mechanism, A is a connection point of the first rod piece and the fixed base, and V is a central point of the winding pulley; l is AS Is the distance S from A, L VS Is the distance S from V, α 0 Is a first rod and L VS Angle between corresponding line segments, alpha 1 Is L VS The included angle h between the corresponding line segment and the connecting segment of the steel wire rope and the first rod piece 0 For the height of the winding pulley mounting, r 0 The radius of the winding pulley is shown, and theta is an included angle between the first rod piece of the parallel mechanism and the normal direction of the fixed base, namely an included angle between the first rod piece and the Z-axis direction;
the relevant parameter comprises a spring stiffness coefficient K 1 And the installation height h of the winding pulley 0 And the position of a connecting point S of the steel wire rope and the first rod piece of the branched chain of the parallel mechanism.
2. The gravity compensation method for the active-passive combined series-parallel force feedback equipment according to claim 1, wherein in the step 1, the quality of a mechanism and a connecting rod of the series-parallel force feedback equipment is simplified according to a statics analysis method, and the method comprises the following specific steps:
1) Simplifying the serial mechanism into mass points acting on the center of the parallel mechanism motion platform;
2) Part of the mass of the second rod piece of each branched chain of the parallel mechanism is attached to the center of the motion platform, and part of the mass is attached to the joint where the first rod piece of each branched chain is connected with the second rod piece;
3) And the second rod piece of each branched chain of the parallel mechanism of the force feedback equipment is equivalent to a two-force rod.
3. The gravity compensation method for the active-passive combined series-parallel force feedback equipment according to claim 1, wherein the step 1 is used for calculating the torque τ consumed by each driving motor when the active gravity compensation is realized based on the torque of the driving motor A The method comprises the following steps:
(1) Firstly, carrying out stress balance analysis on a motion platform of the parallel mechanism to obtain the internal force of a second rod piece in the three branched chains;
(2) Calculating the torque generated by the acting force of the second rod piece on the first rod piece at the rotating joint of the driving motor, the torque generated by the gravity of the first rod piece and the torque generated by the gravity of the second rod piece attached to the first rod piece;
(3) The sum of the three torques obtained in the step (2) is the torque tau consumed by each driving motor during the active gravity compensation A 。
4. The gravity compensation method for the active-passive combined series-parallel force feedback device according to claim 3, wherein the step 2 of optimizing relevant parameters of the spring passive compensation structure comprises the following steps:
s1, setting a motion track of the force feedback equipment along a Z axis of a motion space, wherein the motion track moves from a position close to a fixed base to a position with the maximum Z axis coordinate; obtaining the torque consumed by the three driving motors during the active gravity compensation according to the step 1, wherein the second driving motor and the third driving motor are symmetrically distributed, thereby obtainingThe difference value of the torque consumed by the first driving motor, the second driving motor and the third driving motor is changed along with the included angle theta between the first rod piece of the parallel mechanism and the normal direction of the fixed base, and the curve is used as the target torque tau required to be generated by the spring P ；
s2, torque tau generated by the passive compensation structure for the spring on the branch chain S And the target torque tau required to be generated by the spring P Is integrated to calculate the average torque error tau of the angle change process E ；
s3, mixing tau E The minimum value of the coefficient K is used as an objective function for optimizing related parameters of the spring passive compensation structure to obtain the spring stiffness coefficient K 1 And the installation height h of the winding pulley 0 And the numerical value of a connecting point S of the steel wire rope and the first rod piece of the branched chain of the parallel mechanism.
5. The gravity compensation method for active-passive combined series-parallel force feedback equipment according to claim 1, wherein the torque τ actually required by each driving motor to realize gravity compensation of the force feedback equipment in the corresponding spatial attitude in step 3 is the torque τ consumed by each driving motor during active gravity compensation A Torque tau generated by spring passive compensation structure to branch chain S The formula is obtained as follows:
τ＝[τ A1 -τ S ，τ A2 ，τ A3 ]；
wherein, tau A1 ，τ A2 ，τ A3 Respectively representing the torque, tau, required to be generated by the three driving motors based on the active gravity compensation in step 1 S And (3) representing the torque generated by the spring passive compensation structure on the branch chain in the step (2).
6. The gravity compensation method for the active-passive combined series-parallel force feedback device according to claim 1, wherein the current I in step 4 is a torque τ and a driving motor torque constant K actually required by each driving motor to realize gravity compensation of the force feedback device in a corresponding spatial attitude M The relationship of (a) is obtained, after obtaining the current I, the force feedbackEach branched chain of the equipment drives a motor to output current, so that the force feedback device can keep balance at a spatial position, and the formula is as follows:
Figure FDA0004052225460000031
wherein, K M Is the drive motor torque constant.
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