CN104240263B - A kind of motion subtree system for Delta parallel manipulators - Google Patents

Abstract

The invention discloses a motion feature analysis system for a Delta parallel manipulator, which includes a man-machine interface and an algorithm; the man-machine interface includes an integrated motion feature analysis interface, a cylindrical coordinate inverse calculation mode interface, and a cylindrical coordinate forward calculation mode interface and data output interface; the algorithm includes forward calculation algorithm and inverse calculation algorithm, as well as displacement, velocity, acceleration curve display algorithm and its modules; this system can carry out the mutual positional relationship between the manipulator end actuator and the prime mover according to the forward and inverse calculation algorithm Forward and reverse calculation, output the kinematic feature information of the end element in the form of curves and tables, describe the geometric feature information related to the triangle of the B joint of the Delta parallel manipulator in the form of a space equation, and make a list of system simulation calculation data in TXT format, the B joint is the Delta parallel manipulator The joint of the arm where the upper arm meets the lower arm. The invention can effectively realize the motion characteristic analysis of the Delta parallel manipulator.

Description

A Motion Feature Analysis System for Delta Parallel Manipulator

technical field

The invention relates to the technical field of industrial automation system structure construction and simulation control, in particular to a motion characteristic analysis system for Delta parallel manipulators.

Background technique

Flexible robots (manipulators) are used for intelligent grasping. They generally cooperate with visual imaging and pneumatic execution to achieve grasping actions. They are often used to grasp food (chocolate, candy, biscuits, moon cakes, etc.), electronic components and other materials. Delta agency's efficient logistics solution in three-dimensional space has promoted the upsurge of robot companies from all over the world to develop this agency. So far, the above-mentioned various high-speed parallel manipulators have been applied in the automatic production of electronics, medicine, food and other industries or the operations of sorting, pick-and-place, and packaging in packaging lines.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies and defects of the prior art, and provide a motion characteristic analysis system for Delta parallel manipulators, which can realize the input space cylindrical coordinate data, forward and reverse calculation and output Functions such as end element displacement, velocity and acceleration curves.

In order to achieve the above object, the technical solution provided by the present invention is: a motion characteristic analysis system for Delta parallel manipulators, including two parts of man-machine interface and algorithm made by Visual Basic language; Motion feature analysis interface, cylindrical coordinate inverse calculation mode interface, cylindrical coordinate forward calculation mode interface and data output interface; the algorithm includes forward calculation algorithm and inverse calculation algorithm based on spatial analytic geometry, as well as displacement, velocity, acceleration curve display algorithm and Its modules; the system can perform forward and reverse calculations involving the mutual positional relationship between the end actuator of the manipulator and the prime mover according to the forward and reverse calculation algorithms, output the motion characteristic information of the end components in the form of curves and tables, and describe Delta in the form of space equations Parallel manipulator B joint triangle-related geometric feature information, and make a TXT format system simulation calculation data list, wherein, the B joint is the joint at the connection between the upper arm and the lower arm of the Delta parallel manipulator arm.

Under the integrated motion feature analysis interface, it is possible to input the length of the manipulator arm, the input of the coordinates of the beginning and end positions of the end actuator space, the output of the relative operating angle of the angular displacement driver corresponding to the coordinates of the start and end position columns, and the output of relevant motion feature information;

Input the length of each arm and the coordinates of the start and end positions of the end actuators in the integrated motion feature analysis interface, and the system will first obtain and display the rotation angle of the angular displacement driver through inverse calculation according to the internal integrated forward calculation and inverse calculation algorithms, and then use the inverse Based on the calculation results, assuming that the end actuator is on a straight line segment as the trajectory, calculate and display the initial and final angular displacement values of the three angular displacement drivers. Based on this assumption, calculate and draw the uniform acceleration-constant speed- The three-coordinate displacement, velocity and acceleration curves of the end actuator in the uniform deceleration motion mode.

Under the interface of cylindrical coordinate inverse calculation mode, it is possible to input the length of the manipulator arm, the input of the cylindrical coordinates of the beginning and end positions of the end actuator space, the output of the relative operating angle of the angular displacement driver including two feasible solutions, and the output of the rotation angle-time relationship curve of the three angular displacement drivers. Work;

Enter the length of each arm and the position coordinates of the end actuators on the interface of cylindrical coordinate inverse calculation mode, and two sets of solutions that meet the conditions can be calculated, one of which is an unrealizable singular solution, because the inverse calculation algorithm based on spatial analytic geometry is adopted , the algorithm itself involves trigonometric function equations, so the singular solution is generated. Input the coordinates of the start and end positions of the end actuator, and the angular displacement of the three angular displacement drivers can be calculated and drawn with time.

Under the interface of the cylindrical coordinate forward calculation mode, it is possible to input the starting and ending angles of the angular displacement drive; the output of the triangle geometric characteristics of the B joint, including the output of the plane equation of the B ₁ B ₂ B ₃ joint bearing, the output of the vertical plane equation of B ₁ B ₂ , and the output of the B joint △B ₁ B ₂ B ₃ triangular length output, B joint △B ₁ B ₂ B ₃ circumcircle radius output and B joint △B ₁ B ₂ B ₃ excentric coordinate output, B ₁ , B ₂ , B ₃ Represent the B joints of the three groups of arms of the Delta parallel manipulator; the output of the coordinates of the D point of the center of the end actuator and the output of related motion feature information;

Enter the beginning and end values of the three angular displacement drive angles on the cylindrical coordinate forward calculation mode interface, and the system will follow the normal calculation algorithm according to the B ₁ B ₂ B ₃ joint bearing plane equation, B ₁ B ₂ and B ₂ B ₃ vertical plane equation, △B ₁ B ₂ B ₃ triangular length at B joint, △B ₁ B ₂ B ₃ circumscribed circle radius at B joint and △B ₁ B ₂ B ₃ excentric coordinates at B joint are calculated in order to fully demonstrate the system calculation process, and finally obtain the coordinates of point D of the center of the end effector, and calculate and draw the three-coordinate displacement, velocity and acceleration curves of the end effector.

In the data output interface, it is possible to input the length of the manipulator arm, the input of the moment of inertia of each arm, the input of the mass of each arm, the input of the starting and ending position coordinates of the end actuator, the input of the required movement time, the output of the starting and ending angle of the angular displacement driver, the output of the average speed of the angular displacement driver, Export system simulation calculation data list work;

In the data output interface, input the length of each arm, the moment of inertia of the arm and the mass of the arm, the end actuator, the coordinates of the start and end positions of the end actuator, and the running time. - Assumption of uniform acceleration motion mode Calculate and display the angular displacement driver's uniform motion stage velocity, record several segments in the motion process, each segment's coordinates, speed and acceleration value, and provide the function of outputting TXT data tables.

Both the integrated motion feature analysis interface and the cylindrical coordinate positive calculation interface have the function of outputting the three-coordinate direction displacement, velocity and acceleration curve of the terminal actuator, which adopts the Graphics graphics drawing method in the VB program, and provides a comparison of the displayed curves. The function of adjusting the scale of the coordinate axis, the interface of the cylindrical coordinate reverse calculation mode and the cylindrical coordinate forward calculation mode interface provide an interface for separating the forward calculation and the reverse calculation.

The inverse is the cylindrical coordinate of the spatial position of the input terminal actuator, and the motor movement angle is calculated through an algorithm, and the algorithm is as follows:

The program uses cylindrical coordinates to calculate, and the initial value of the custom angle is 30 degrees. The following variables are explained: l ₁ is the OA distance, l ₂ is the length of the upper arm, l ₃ is the length of the lower arm, and l ₄ is three joints from the center of the end actuator Bearing distance, dx is the angle variable defined by the center of the end actuator, dy is the radius variable defined by the center of the end actuator, dz is the height variable defined by the center of the end actuator, is the angle between the upper arm and the horizontal direction, opA, opB, opC are The three constants of the equation are calculated from known conditions;

Linear motion calculation:

Assume moving from (θ ₁ , r1, h1) to (θ ₂ , r2, h2), the motor is rotating the cylindrical coordinates at a constant speed

Cartesian coordinates

Let the coordinates of point D be D(θ _D , r _D , h _D )

Design coordinate transfer program

Cartesian

where the range r _D ≤ 131.18, h _D ≤ 244.18

Apply the distance formula to the two points BC (where is unknown)

expand

Simplify 1

Simplify 2

Simplify 3

Three groups of arms apply the same process for simplification

Solve the above trigonometric function equation opA sinθ+opB cosθ+opC=0

Apply the formula

Solvable

The inverse calculation data obtained by the forward calculation, assuming that the end actuator is uniformly accelerated, uniformly accelerated, and uniformly decelerated from the starting point in space in a straight line, after calculating the displacement, velocity and acceleration during the period, the calculation data can be selectively output or It is displayed in the form of s-t, v-t, a-t diagram, and its algorithm is as follows:

Cylindrical coordinates

Cartesian coordinates

A point in space is at the same distance from B1, B2, and B3, and B1, B2, and B3 respectively represent the B joints of the three groups of arms of the Delta parallel manipulator,

Determine the center of the circumcircle of B1, B2, B3

circumcircle radius

semicircle length

helen formula

Among them, abc is the length of three sides, which is obtained by the formula of space distance;

The formula for the coordinates of the center of the circumscribed circle is as follows:

radius

Increments are defined using the method of direction vectors

Suppose two points (x1, y1, z1) and (x2, y2, z2), the direction vector is (x2-x1, y2-y1, z2-z1)

The increments in each direction can be defined as

There are two points (θ ₁ ,r ₁ ,h ₁ ) and (θ ₂ ,r ₂ ,h ₂ ) in cylindrical coordinates

Direction vector (r ₂ cosθ ₂ -r ₁ cosθ ₁ ,r ₂ sinθ ₂ -r ₁ sinθ ₁ ,h ₂ -h ₁ )

The direction vector to cylindrical coordinates is as follows:

The direction increment should be:

The direction vector is defined in the program as vic, that is, the vector victor

The cylindrical coordinates represented by Cartesian coordinates are dex, dey, dez

Then there are initial values dex=r ₁ cosθ ₁ , dey=r ₁ sinθ ₁ , dez=h ₁

There are increments deltax, deltay, deltaz in each direction

and is a fixed value

Array of equations:

Use the b array directly for easy viewing, and replace the array with bb and bbb first

After the B plane equation has been solved, the B1B2, B2B3, and B3B1 direction cosine matrices can be obtained

According to the nature of the circumcenter of a triangle, the circumcenter O should be in the plane intersection of three planes

Solve the ternary linear equation again

Attached direction cosine method:

Using the vector method, it is known that the hand movement characteristic is only translation, so the Translating a certain distance towards the center of the hand can form a characteristic geometry similar to a ball,

The three translation vectors are The translation distance is l ₄ , and the translation vector is MOVE(3,3)

The MOVE matrix is

Point B is translated to the vector, add the matrix, pay attention to pay back;

The translation transformation adopts the four-dimensional matrix multiplication transformation

The coordinates of point B need to add one dimension, the basic method is as follows:

Calculate the coordinates of the center of the circumscribed circle of the triangle according to the above method

half circumference

helen formula

circumcircle radius

Find the OD straight line expression, the vertical plane B1B2B3 and the direction vector passing through D can be expressed, and the direction vector advances The length is the position of point D.

The system includes a single-arm set characteristic input module of the Delta parallel manipulator, through which the size characteristics of the Delta parallel manipulator used for internal calculation can be changed, and then can be used to calculate the optimal solution of the Delta parallel manipulator with acceleration as an index.

The system includes a calculation result display module, the calculation result display module is attached with a scale definition box, and the display of graph lines in coordinates can be controlled by defining the scale size.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

This system can effectively realize the analysis of the motion characteristics of the Delta parallel manipulator, and can realize the input of spatial cylindrical coordinate data, the forward and reverse calculation of the position of the actuator at the end of the manipulator and the prime mover, the output of the motion characteristic information of the end element, and the related geometric characteristics of the B-joint triangle of the Delta parallel manipulator. Information, system simulation calculation data list and other functions; the system includes the output data list function of B joint triangle geometric characteristics, angular displacement driver geometric characteristics, etc., which can provide a more convenient way for the analysis of the motion characteristics of Delta parallel manipulators, and provide a more convenient way for the later analysis of Delta structures. The determination and optimization of the geometric relationship provide the basis; the cylindrical coordinate inverse calculation mode interface and the cylindrical coordinate forward calculation mode interface provide a man-machine interface that separates the forward calculation and the reverse calculation, and can be used as a teaching software for college students to learn parallel manipulators. Students deeply understand the significance of forward and reverse calculation of parallel manipulators; this system can change the length of each arm of parallel manipulators, combined with the data list of simulation calculation results of this system, can cooperate with statistical methods to solve the optimal solution of manipulator length under the condition of minimum acceleration.

Description of drawings

Figure 1 is a schematic diagram of a Delta parallel manipulator.

Figure 2 is an interface diagram of integrated motion feature analysis including calculation results.

Figure 3 is an interface diagram of the cylindrical coordinate inversion method including the calculation results.

Figure 4 is an interface diagram of the cylindrical coordinate forward calculation method including the calculation results.

Figure 5 is a diagram of the data output interface including calculation results.

Fig. 6 is a data list document diagram of the calculation result of the data output interface.

detailed description

The present invention will be further described below in conjunction with specific examples.

The motion characteristic analysis system that is used for Delta parallel manipulator described in the present embodiment comprises man-machine interface and algorithm two parts made by VisualBasic language; Wherein, described man-machine interface comprises integrated motion characteristic analysis interface (SIM interface), Cylindrical Coordinate-Inverse Solution Interface, Cylindrical Coordinate-Positive Solution Interface, and Data Output Interface (Motor Interface); the algorithm includes a forward calculation algorithm based on spatial analytic geometry And back calculation algorithm, as well as displacement, velocity, acceleration curve display algorithm and its modules.

The system can perform forward and reverse calculations involving the mutual positional relationship between the end actuator of the manipulator and the prime mover according to the forward and inverse calculation algorithm, output the motion characteristic information of the end element in the form of curves and tables, and describe the Delta parallel manipulator B in the form of space equations Joint triangle-related geometric feature information, and make a TXT format system simulation calculation data list, wherein the B joint is the joint at the connection between the upper arm and the lower arm of the Delta parallel manipulator arm, as shown in Figure 1.

Under the integrated motion feature analysis interface, it is possible to input the length of the manipulator arm, the input of the coordinates of the beginning and end positions of the end actuator space, the output of the relative operating angle of the angular displacement driver corresponding to the coordinates of the start and end position columns, and the output of relevant motion characteristic information (curves), etc. ;

Input the length of each arm and the coordinates of the start and end positions of the end actuators in the integrated motion feature analysis interface, and the system will first obtain and display the rotation angle of the angular displacement driver through inverse calculation according to the internal integrated forward calculation and inverse calculation algorithms, and then use the inverse Based on the calculation results, assuming that the end actuator is on a straight line segment as the trajectory, calculate and display the initial and final angular displacement values of the three angular displacement drivers. Based on this assumption, calculate and draw the uniform acceleration-constant speed- The three-coordinate displacement, velocity and acceleration curves of the terminal actuator in the uniform deceleration mode are shown in Figure 2.

Under the interface of cylindrical coordinate inverse calculation mode, it is possible to input the length of the manipulator arm, the input of the cylindrical coordinates of the beginning and end positions of the end actuator space, the output of the relative operating angle of the angular displacement driver including two feasible solutions, and the output of the rotation angle-time relationship curve of the three angular displacement drivers. waiting for work;

Enter the length of each arm and the position coordinates of the end actuators on the interface of cylindrical coordinate inverse calculation mode, and two sets of solutions that meet the conditions can be calculated, one of which is an unrealizable singular solution, because the inverse calculation algorithm based on spatial analytic geometry is adopted , the algorithm itself involves trigonometric function equations, so the singular solution is generated. Input the starting and ending position coordinates of the end actuator, and the angular displacement of the three angular displacement drivers can be calculated and drawn over time, as shown in Figure 3.

Under the interface of the cylindrical coordinate forward calculation mode, it is possible to input the starting and ending angles of the angular displacement drive; the output of the triangle geometric characteristics of the B joint, including the output of the plane equation of the B ₁ B ₂ B ₃ joint bearing, the output of the vertical plane equation of B ₁ B ₂ , and the output of the B joint △B ₁ B ₂ B ₃ triangular length output, B joint △B ₁ B ₂ B ₃ circumcircle radius output and B joint △B ₁ B ₂ B ₃ excentric coordinate output, B ₁ , B ₂ , B ₃ Represent the B joints of the three groups of arms of the Delta parallel manipulator; the output of the coordinates of the D point of the center of the end actuator and the output of related motion characteristic information (curves), etc.;

Enter the beginning and end values of the three angular displacement drive angles on the cylindrical coordinate forward calculation mode interface, and the system will follow the normal calculation algorithm according to the B ₁ B ₂ B ₃ joint bearing plane equation, B ₁ B ₂ and B ₂ B ₃ vertical plane equation, △B ₁ B ₂ B ₃ triangular length at B joint, △B ₁ B ₂ B ₃ circumscribed circle radius at B joint and △B ₁ B ₂ B ₃ excentric coordinates at B joint are calculated in order to fully demonstrate the system calculation process, and finally obtain the coordinates of point D in the center of the end effector, and calculate and draw the three-coordinate displacement, velocity and acceleration curves of the end effector, as shown in Figure 4.

In the data output interface, it is possible to input the length of the manipulator arm, the input of the moment of inertia of each arm, the input of the mass of each arm, the input of the starting and ending position coordinates of the end actuator, the input of the required movement time, the output of the starting and ending angle of the angular displacement driver, the output of the average speed of the angular displacement driver, Export the list of system simulation calculation data, etc.;

In the data output interface, input the length of each arm, the moment of inertia of the arm and the mass of the arm, the end actuator, the coordinates of the start and end positions of the end actuator, and the running time. - Assumption of uniform acceleration motion method Calculate and display the angular displacement driver's uniform motion stage velocity, record several segments in the motion process, each segment's coordinates, speed and acceleration value, and provide the function of outputting TXT data tables, as shown in Figure 5 and shown in Figure 6.

Both the integrated motion feature analysis interface and the cylindrical coordinate positive calculation interface have the function of outputting the three-coordinate direction displacement, velocity and acceleration curve of the terminal actuator, which adopts the Graphics graphics drawing method in the VB program. According to the characteristics of the display method , in order to enable the user to better observe the curve, this drawing method provides the function of adjusting the scale of the relative axis of the displayed curve. The cylindrical coordinate inverse calculation mode interface and cylindrical coordinate forward calculation mode interface provide an interface that separates forward calculation and inverse calculation, and can be used as teaching software for college students to learn parallel manipulators, so that students can deeply understand the meaning of forward and inverse calculations of parallel manipulators .

The inverse is to input the cylindrical coordinates of the spatial position of the end actuator, and calculate the motor movement angle through an algorithm. Its algorithm is as follows:

The program uses cylindrical coordinates to calculate, and the initial value of the custom angle is 30 degrees. The following variables are explained: l ₁ is the OA distance, l ₂ is the length of the upper arm, l ₃ is the length of the lower arm, and l ₄ is three joints from the center of the end actuator Bearing distance, dx is the angle variable defined by the center of the end actuator, dy is the radius variable defined by the center of the end actuator, dz is the height variable defined by the center of the end actuator, is the angle between the upper arm and the horizontal direction, opA, opB, opC are The three constants of the equation are calculated from known conditions;

Linear motion calculation:

Assume that the motor is rotating at a constant speed when moving from (θ ₁ , r1, h1) to (θ ₂ , r2, h2)

Cylindrical coordinates

Cartesian coordinates

Let the coordinates of point D be D(θ _D , r _D , h _D )

Design coordinate transfer program

Cartesian

where the range r _D ≤ 131.18, h _D ≤ 244.18

Apply the distance formula to the two points BC (where is unknown)

expand

Simplify 1

Simplify 2

Simplify 3

Three groups of arms apply the same process for simplification

Solve the above trigonometric function equation opA sinθ+opB cosθ+opC=0

Apply the formula

Solvable

During inverse calculation, after the user inputs the dimensional characteristics of the Delta parallel manipulator and the spatial position cylindrical coordinates of the end actuator, the system converts the input starting point coordinates and end point coordinates into space vectors, and brings in the unknown motor rotation angle to calculate the manipulator using the spatial geometric relationship The coordinates of the joints of the arm, the three coordinates obtained by this calculation are respectively combined with the start coordinates and the end coordinates to form a coordinate formula between two points. The obtained two sets of three ternary quadratic equations will be obtained through a set of simplification steps to obtain a rational calculation formula about the tangent of the motor rotation angle. The final calculation result is obtained through the trigonometric calculation module. The motion angle of the motor is calculated by this algorithm. In industrial control, the angle information and other related motion characteristics can be input into the motion control module to achieve the purpose of controlling the end element to move according to the specified path.

The inverse calculation data obtained by the forward calculation, assuming that the end actuator is uniformly accelerated, uniformly accelerated, and uniformly decelerated from the starting point in space in a straight line, after calculating the displacement, velocity and acceleration during the period, the calculation data can be selectively output or Displayed in the form of s-t, v-t, a-t diagram. Its algorithm is as follows:

Cylindrical coordinates

Cartesian coordinates

A point in space is at the same distance from B1, B2, and B3, and B1, B2, and B3 respectively represent the B joints of the three groups of arms of the Delta parallel manipulator,

Determine the center of the circumcircle of B1, B2, B3

circumcircle radius

semicircle length

helen formula

Among them, abc is the length of three sides, which is obtained by the formula of space distance;

The formula for the coordinates of the center of the circumscribed circle is as follows:

radius

Increments are defined using the method of direction vectors

Suppose two points (x1, y1, z1) and (x2, y2, z2), the direction vector is (x2-x1, y2-y1, z2-z1)

The increments in each direction can be defined as

There are two points (θ ₁ ,r ₁ ,h ₁ ) and (θ ₂ ,r ₂ ,h ₂ ) in cylindrical coordinates

Direction vector (r ₂ cosθ ₂ -r ₁ cosθ ₁ ,r ₂ sinθ ₂ -r ₁ sinθ ₁ ,h ₂ -h ₁ )

The direction vector to cylindrical coordinates is as follows:

The direction increment should be:

The direction vector is defined in the program as vic, that is, the vector victor

The cylindrical coordinates represented by Cartesian coordinates are dex, dey, dez

Then there are initial values dex=r ₁ cosθ ₁ , dey=r ₁ sinθ ₁ , dez=h ₁

There are increments deltax, deltay, deltaz in each direction

and is a fixed value

Array of equations:

Use the b array directly for easy viewing, and replace the array with bb and bbb first

After the B plane equation has been solved, the B1B2, B2B3, and B3B1 direction cosine matrices can be obtained

According to the nature of the circumcenter of a triangle, the circumcenter O should be in the plane Solve the ternary linear equation again at the intersection of three planes

Attached direction cosine method:

Using the vector method, it is known that the hand movement characteristic is only translation, so the Translating a certain distance towards the center of the hand can form a characteristic geometry similar to a ball,

The three translation vectors are The translation distance is l ₄ , and the translation vector is MOVE(3,3)

The MOVE matrix is

Point B is translated to the vector, add the matrix, pay attention to pay back;

The translation transformation adopts the four-dimensional matrix multiplication transformation

The coordinates of point B need to add one dimension, the basic method is as follows:

Calculate the coordinates of the center of the circumscribed circle of the triangle according to the above method

half circumference

helen formula

circumcircle radius

Find the OD straight line expression, the vertical plane B1B2B3 and the direction vector passing through D can be expressed, and the direction vector advances The length is the position of point D.

In the forward calculation, the obtained inverse calculation data is used as the initial data, and according to the motion mode defined by the user (in this program, it is defined as the motion characteristics of uniform acceleration, uniform speed, and uniform deceleration), assuming that the end actuator moves from the starting point in space to the The end point, from which the motion vectors of the three joints can be established. The motion vectors at the joints are stored in a matrix, and will be discretized, and the degree of discretization is determined by the precision required by the calculation. By using this method, a series of coordinates located on the motion vector and between the starting and ending points of the joints will be obtained. Each set of joint coordinates is a point on a sphere with the end actuator as the center and the length of the lower rod as the radius. Calculate the circumcenter and circumcircle radius of the joint point triangle through Heron's formula, and it is not difficult to prove that the connecting line between the excenter and the end actuator is perpendicular to the plane where the three points are located. The height coordinate can be obtained by using the method of solving the space triangle, and the other two coordinates can be calculated by simple geometry. Velocity and acceleration are also calculated in a similar fashion. After calculating the displacement, velocity and acceleration during the period, the calculation data can be selectively output or displayed in the form of s-t, v-t, a-t diagram.

The output mode of graphics plus data can make it more convenient and comprehensive for users to understand the process of forward calculation and reverse calculation algorithm, deeply understand the essence of algorithm, and achieve better teaching effect.

In addition, this system also provides a Delta parallel manipulator single-arm set feature input module and a calculation result display module. Through the Delta parallel manipulator single-arm set feature input module, the size characteristics of the Delta parallel manipulator used for internal calculations can be changed, and then it can be used for calculation. The optimal solution of the Delta parallel manipulator with acceleration as the index provides a basis for designers to determine the size of the arm. The calculation result display module is attached with a scale definition box, and the display of graph lines in coordinates can be controlled by defining the size of the scale.

The embodiments described above are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Therefore, all changes made according to the shape and principles of the present invention should be covered within the protection scope of the present invention.

Claims (8)

1. a kind of motion subtree system for Delta parallel manipulators, it is characterised in that：Including by Visual Basic Man machine interface and algorithm two large divisions that language makes；The man machine interface includes integrating motion subtree interface, cylindrical coordinatess Inverse mode interface, cylindrical coordinatess are just calculating mode interface and data output interface；The algorithm is included based on interspace analytic geometry Just algorithm and inverse algorithm, and displacement, speed, accelerating curve display algorithm and its module；The system being capable of basis Positive and negative computation algorithm carries out the positive inverse for being related to arm end executive component and prime mover mutual alignment relation, with curve and table The mode of lattice exports end component body dynamics information, and Delta parallel manipulators B joint triangle is described in the form of space equation Shape correlation geometric properties information, and make TXT format system simulation calculus data lists, wherein, the B joints be Delta simultaneously The upper arm of connection manipulator arm and the joint of underarm junction；The inverse is that the locus post for being input into final actuating element is sat Mark, calculates motor movement angle by algorithm, and its algorithm is as follows：

Inside program using cylindrical coordinatess calculate, self-defined angle initial value be 30 degree, below variable declaration：l₁For OA distances, l₂For upper Arm lengths, l₃For lower arm lengths, l₄For the distance of three oscillating bearings of final actuating element centre-to-centre spacing, dx is final actuating element The angle variables of center definition, radius variables of the dy for the definition of final actuating element center, dz are fixed for final actuating element center The height variable of justice,For upper arm and horizontal direction angle, opA, opB, opC areThree constants of equation, by known conditions meter Draw；

Rectilinear motion mode is calculated：

If from (θ₁, r1, h1) and move to (θ₂, r2, h2), motor is just in uniform rotation

Cylindrical coordinatess

Cartesian coordinate

If D point coordinates is D (θ_D, r_D, h_D)

Design coordinate branching program

Descartes

Wherein scope r_D≤ 131.18, h_D≤244.18

To 2 points of applications distances formula of BC, whereinFor unknown number

$\begin{array}{c}{\[r_D{\mathrm{cos\θ}}_D+l_{4}cos\mathrm{\θ}-(l_1+l_{2}cos{\∂}_1)cos0\]}^2+{\[r_D{\mathrm{sin\θ}}_D+l_{4}sin0-(l_1+l_{2}cos{\∂}_1)sin0\]}^2+{(h_D-l_{2}sin{\∂}_1)}^2\\ =l_3^2\end{array}$

Launch

$\begin{array}{c}{\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)}^2+{\[\left(l_1+l_2\cos {\∂}_1\right)\cos 0\]}^2-2\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)\left(l_1+l_2\cos {\∂}_1\right)\cos 0\\ +{\left(r_D{\mathrm{sin\θ}}_D+l_4\sin 0\right)}^2+{\[\left(l_1+l_2\cos {\∂}_1\right)\sin 0\]}^2-2\left(r_D{\mathrm{sin\θ}}_D+l_4\sin 0\right)\left(l_1+l_2\cos {\∂}_1\right)\sin 0\\ +h_D^2+{\left(l_2\sin {\∂}_1\right)}^2-2h_D{l}_2\sin {\∂}_1-l_3^2=0\end{array}$

Abbreviation 1

$\begin{array}{c}{\left(l_1+l_2\cos {\∂}_1\right)}^2+{\left(l_2\sin {\∂}_1\right)}^2-2\[r_D{\mathrm{cos\θ}}_D\cos 0+l_4{\cos }^{2}0+r_D{\mathrm{sin\θ}}_D\sin 0+l_4{\sin }^{2}0\]\left(l_1+l_2\cos {\∂}_1\right)\\ -2h_D{l}_2\sin {\∂}_1+{\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)}^2+{\left(r_D{\mathrm{sin\θ}}_D+l_4\sin 0\right)}^2+h_D^2-l_3^2=0\end{array}$

Abbreviation 2

$\begin{array}{c}{l}_1^2+l_2^2+2l_1{l}_{2}cos{\∂}_1-2(r_D{\mathrm{cos\θ}}_{D}cos0+r_D{\mathrm{sin\θ}}_{D}sin0+l_4^2)(l_{2}cos{\∂}_1+l_1)-h_D{l}_{2}sin{\∂}_1+\\ \mathrm{......}\end{array}$

Abbreviation 3

$\begin{array}{c}2l_2(r_D{\mathrm{cos\θ}}_{D}cos0+r_D{\mathrm{sin\θ}}_{D}sin0+l_4^2+l_1)cos{\∂}_1-2h_D{l}_{2}sin{\∂}_1+l_1^2+l_2^2\\ -2l_1\left(r_D{\mathrm{cos\θ}}_D\cos 0+r_D{\mathrm{sin\θ}}_D+{l_4}^2\right)+{\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)}^2+{\left(r_D{\mathrm{sin\θ}}_D+R_4\sin 0\right)}^2+h_D^2-l_3^2=0\end{array}$

Three groups of same processes of arm application carry out abbreviation

Solve above-mentioned trigonometric function equation opA sin θs+opB cos θ+opC=0

Using formula

$tan\left(\frac{\∂}{2}\right)=\frac{A\±\sqrt{A^2+B^2-C^2}}{B-C}$

Can solve

The inverse data just at last by obtaining, it is assumed that final actuating element adds from space starting point is even in a linear fashion Speed, at the uniform velocity, in the case of even deceleration, during calculating after displacement, speed and acceleration, can with selectivity output calculate data or with The form of s-t, v-t, a-t figure shows that its algorithm is as follows：

Cylindrical coordinatess

Cartesian coordinate

Distance of the space a little away from B1, B2, B3 is equal, and B1, B2, B3 represent the B of three groups of arms of Delta parallel manipulators respectively Joint,

Determine B1, B2, the B3 circumscribed circle center of circle

Circumradius

Semicircle is long

Heron's formula

$R=\frac{abc}{\sqrt{(a+b+c)(a+b-c)(a-b+c)(-a+b+c)}}$

Wherein abc is three length of sides, by obtained by space length formula；

Circumscribed circle central coordinate of circle formula is as follows：

$A=\sqrt{{(Xa-Xb)}^2+{(Ya-Yb)}^2}$

$B=\sqrt{{(Xa-Xc)}^2+{(Ya-Yc)}^2}$

$C=\sqrt{{(Xb-Xc)}^2+{(Yb-Yc)}^2}$

$Y=\frac{A+B+C}{2}$

$X=\sqrt{Y(Y-A)(Y-B)(Y-C)}$

Radius

Increment is defined using the method for direction vector

If 2 points (x1, y1, z1) and (x2, y2, z2), its direction vector is (x2-x1, y2-y1, z2-z1)

All directions increment may be defined as

Circular cylindrical coordinate divides into 2 points of (θ₁,r₁,h₁) and (θ₂,r₂,h₂)

Direction vector (r₂cosθ₂-r₁cosθ₁,r₂sinθ₂-r₁sinθ₁,h₂-h₁)

It is as follows that direction vector turns circular cylindrical coordinate：

$\left(\arctan \left(\frac{r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1}{r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1}\right),\sqrt{{\left(r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1\right)}^2+{\left(r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1\right)}^2},h_2-h_1\right)$

Direction increment should be：

$\left(\arctan \right(\frac{r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1}{r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1}),\frac{\sqrt{{(r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1)}^2+{(r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1)}^2}}{n},\frac{h_2-h_1}{n})$

Defined in program, direction vector is vic, i.e. vector v ictor

The cylindrical coordinatess that cartesian coordinate is represented be dex, dey, dez

Then there is initial value dex=r₁cosθ₁, dey=r₁sinθ₁, dez=h₁

There are all directions increment deltax, deltay, deltaz

And be definite value

$deltaz=\frac{h_2-h_1}{n}$

Equation array：

B arrays are directly adopted, is conveniently checked, conversion array is first replaced with bb and bbb

B plane equations are solved, has then tried to achieve B1B2, B2B3, B3B1 direction cosine matrixAccording to three Angular unfaithful intention property, unfaithful intention O should be in planeThree plane crossing places solve ternary first power again Journey

Attached direction cosines seek method：

$cos{\∂}_1=\frac{x_{B2}-x_{B1}}{\left|B1B2\right|}$

${\mathrm{cos\β}}_1=\frac{y_{B2}-y_{B1}}{\left|B1B2\right|}$

${\mathrm{cosv}}_1=\frac{z_{B2}-z_{B1}}{\left|B1B2\right|}$

Using vector method, it is known that hand exercise characteristic is only translation, therefore willCan be formed to hand center translation certain distance The feature geometries body of similar ball,

Three translation vectors areTranslation distance is l₄If, translation vector be MOVE (3,3) MOVE matrixes be

B points are made matrix addition, note paying back toward vector translation；

Translation transformation adopts four-matrix multiplication transformations

B point coordinates need to increase one-dimensional, and basic skills is as follows：

$\left[\begin{array}{cccc}x& y& z& 1\end{array}\right]\×\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ m& n& p& 1\end{array}\right]=\left[\begin{array}{cccc}x+m& y+n& z+p& 1\end{array}\right]$

Triangle circumcenter coordinate is asked for according to said method

Semi-perimeter

Heron's formula

Circumradius

The direction vector for asking for OD straight line expression formulas, vertical plane B1B2B3 and D excessively can represent that direction vector advances Length, as D point position.

2. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Manipulator arm length input, final actuating element space whole story position can be carried out in the case where motion subtree interface is integrated Cylindrical coordinatess input, the relative angle of operation of the angular displacement driver corresponding with whole story position cylindrical coordinatess are exported, relative motion feature Information output works；

It is input into each arm length and final actuating element whole story position coordinateses in the case where motion subtree interface is integrated, system will be by The just calculation integrated according to inside and inverse algorithm, first pass through the corner that inverse is obtained and shows angular displacement driver, then with this Based on inverse result, it is assumed that final actuating element is, with straightway as track, three angular displacement drivers to be calculated and displayed Whole story angular displacement numerical value, based on being assumed by this, calculate and draw out in the specified time according to even acceleration-at the uniform velocity-even deceleration Three coordinate direction displacement of final actuating element, speed and accelerating curve during motion mode.

3. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Manipulator arm length input, final actuating element space whole story position column can be carried out under cylindrical coordinatess inverse mode interface Coordinate input, the relative angle of operation output of the angular displacement driver comprising two kinds of feasible solutions, three angular displacement drivers corner-when Between relation curve output services；

Each arm length and final actuating element position coordinateses are input at cylindrical coordinatess inverse mode interface, can be calculated and be met bar Two groups of solutions of part, one of which solution are not attainable singular solution, due to adopting the inverse algorithm based on interspace analytic geometry, Algorithm is related to trigonometric function equation in itself, thus generates the singular solution, is input into final actuating element whole story position coordinateses, can The angular displacement for calculating and drawing out three angular displacement drivers changes over curve.

4. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Just calculating in cylindrical coordinatess and can carry out under mode interface the input of angular displacement driver whole story corner；B joints triangle geometry feature is defeated Go out, including B₁B₂B₃The output of oscillating bearing plane equation, B₁B₂The output of middle vertical plane equation, B joint △ B₁B₂B₃The output of three length of sides, B Joint △ B₁B₂B₃Circumradius is exported and B joint △ B₁B₂B₃Unfaithful intention coordinate is exported, B₁、B₂、B₃Delta is represented respectively The B joints of three groups of arms of parallel manipulator；The D point coordinates output of final actuating element center and relative motion characteristic information are exported Work；

The whole story numerical value that mode interface is input into three angular displacement driver angles is being calculated just in cylindrical coordinatess, system will be according to just algorithm According to B₁B₂B₃Oscillating bearing plane equation, B₁B₂And B₂B₃Middle vertical plane equation, B joint △ B₁B₂B₃Three length of sides, B joint △ B₁B₂B₃Circumradius and B joint △ B₁B₂B₃The order of unfaithful intention coordinate is calculated, abundant display systems calculating process, most The coordinate of final actuating element center D points is drawn afterwards, and is calculated and drawn out three coordinate direction displacement of final actuating element, speed Degree and accelerating curve.

5. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Can carry out under data output interface manipulator arm length input, inertia of respectively rolling over input, each arm mass input, Final actuating element whole story position coordinateses are input into, require movement time input, the output of angular displacement driver whole story angle, angular displacement The output of driver Mean Speed, guiding system simulation calculus data list work；

Each arm length is input under data output interface, inertia is rolled over and arm, final actuating element quality, end are held Units whole story position coordinateses and run time, system will be according to final actuating elements with straightway as track, and angular displacement drives The hypothesis of the even acceleration of device-at the uniform velocity-uniformly accelerated motion mode is calculated and be shown angular displacement driver uniform motion stage speed, record Some segmentations in motor process, the coordinate of each segmentation, speed and accekeration, and the function of output TXT data forms is provided.

6. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：The integration motion subtree interface and cylindrical coordinatess are just being calculated mode interface and are being owned by exporting three coordinate side of final actuating element To the function of displacement, speed and accelerating curve, the Graphics graphic plotting modes in VB programs are which employs, and provides right Show the function that the scale of curve relative coordinates axle is adjusted；The cylindrical coordinatess inverse mode interface and the cylindrical coordinatess just side of calculation Formula interface provides just calculates the interface being separated with inverse.

7. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：The system includes Delta parallel manipulator single armed set feature input modules, can change internal calculation by the module With the size characteristic of Delta parallel manipulators, and then can be used to calculating Delta parallel manipulators with acceleration as index most Excellent solution.

8. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：The system includes result of calculation display module, and the result of calculation display module defines frame with scale, can be by fixed Adopted scale size controls display of the figure line in coordinate.