A high-precision and large-load redundant six-degree-of-freedom parallel mechanism

Abstract

The present invention relates to a high-precision large-load redundant six-degree-of-freedom parallel mechanism, belonging to the technical field of parallel robots; the moving platform is horizontally and coaxially arranged above the fixed platform; six active drive chains are arranged between the fixed platform and the moving platform to connect the fixed platform and the moving platform; the bottom ends of the six active drive chains are circumferentially distributed along the fixed platform; the top ends of the six active drive chains are circumferentially distributed along the moving platform; six follower redundant measurement chains are arranged between the fixed platform and the moving platform to connect the fixed platform and the moving platform; the bottom ends of the six follower redundant measurement chains are circumferentially distributed along the fixed platform; the top ends of the six follower redundant measurement chains are circumferentially distributed along the moving platform; the six active drive chains are located on the circumferential outer side of the six follower redundant measurement chains; the present invention overcomes the defect that the precision of the traditional six-degree-of-freedom parallel mechanism is affected when carrying a large load, and realizes the high-precision movement of the large-load six-degree-of-freedom parallel mechanism.

Description

Technical Field

[0001] The invention belongs to the technical field of parallel robots and relates to a high-precision large-load redundant six-degree-of-freedom parallel mechanism. Background Art

[0002] For large-aperture optical telescopes on the ground or in space, there are problems that the misalignment of the poses and the surface shape errors of large-load optical components affect the imaging quality. Experts and scholars at home and abroad mainly adopt active optics and adaptive optics to solve this problem, that is, adding precise active adjustment control devices that can be used for precise relative pose adjustment in the optoelectronic payload system. In addition, further aiming at the implementation form of the segmented ultra-large-aperture primary mirror, the segmented primary mirror and the secondary mirror are cooperatively adjusted to correct the optical field aberration. For example, the end adjustment devices of the secondary mirror and 18 primary mirrors with the highest pose adjustment accuracy requirements in the JWST system all adopt precise active adjustment control devices with an accuracy of up to hundreds of nanometers to perform the relative pose correction between optical components. The spatial degrees of freedom for the high-precision active adjustment of the poses of the primary and secondary mirrors of large-aperture optical payloads in orbit are five to six, belonging to high-precision multi-degree-of-freedom adjustment. Through the spatial multi-degree-of-freedom adjustment device, the pose relationships of the components of the optical detection system can be restored to the ideal state, so as to meet the application requirements of high-resolution imaging of the system. Therefore, the multi-degree-of-freedom precise active adjustment control device is the key actuator for realizing active optics and adaptive optics of large-aperture high-performance optical payloads on the ground and in space.

[0003] In terms of engineering implementation, parallel mechanisms are generally used at home and abroad to achieve six-degree-of-freedom high-precision pose adjustment. The traditional six-degree-of-freedom adjustment device is composed of four major parts: a moving platform, 6 retractable active drive chains, 12 universal hinges, and a static platform. The static platform is fixed, the moving platform is connected to the load, and the platform and the active drive chains are linked by hinges. The telescopic movement of the support rods is driven by motors to realize the translation of the moving platform along the x, y, and z axes and the rotation U, V, and W movements around the x, y, and z axes.

[0004] However, with the increasing requirements for imaging resolution, the aperture of the telescope is also getting larger, and large loads generate large interference forces at different poses, making the active drive chains of the parallel mechanism significantly affected by impact forces during operation. The deformation of the hinges and the active drive chains will affect the measurement accuracy of the active drive chains, and the pose control of the six-degree-of-freedom parallel mechanism depends on the measurement accuracy of the positions of the active drive chains, which affects the pose accuracy of the traditional six-degree-of-freedom parallel mechanism. Summary of the Invention

[0005] The technical problem solved by the invention is: overcoming the deficiencies of the prior art, a high-precision large-load redundant six-degree-of-freedom parallel mechanism is proposed, which overcomes the defect that the accuracy of the traditional six-degree-of-freedom parallel mechanism is affected when carrying large loads, and realizes the high precision of the large-load six-degree-of-freedom parallel mechanism.

[0006] The technical solution of the present invention is as follows:

[0007] A high-precision large-load redundant six-degree-of-freedom parallel mechanism includes a fixed platform, a moving platform, 6 active driving chains, and 6 follow-up redundant measuring chains; wherein, the fixed platform is a horizontally placed frustum structure; the moving platform is horizontally and coaxially arranged above the fixed platform; the 6 active driving chains are arranged between the fixed platform and the moving platform, connecting the fixed platform and the moving platform; the bottom ends of the 6 active driving chains are circumferentially distributed along the fixed platform; the top ends of the 6 active driving chains are circumferentially distributed along the moving platform; the 6 follow-up redundant measuring chains are arranged between the fixed platform and the moving platform, connecting the fixed platform and the moving platform; the bottom ends of the 6 follow-up redundant measuring chains are circumferentially distributed along the fixed platform; the top ends of the 6 follow-up redundant measuring chains are circumferentially distributed along the moving platform; the 6 active driving chains are located on the circumferential outer side of the 6 follow-up redundant measuring chains; the top end of the active driving chain is connected to the moving platform through a hinge, and the bottom end of the active driving chain is connected to the fixed platform through a hinge; the top end of the follow-up redundant measuring chain is connected to the moving platform through a spherical hinge, and the bottom end of the follow-up redundant measuring chain is connected to the fixed platform through a spherical hinge.

[0008] In the above-mentioned high-precision large-load redundant six-degree-of-freedom parallel mechanism, the intersections of the top ends of the 6 active driving chains and the moving platform form a circle, the intersections of the top ends of the 6 follow-up redundant measuring chains and the moving platform form a circle, and the two circles are concentric with the center p; the intersections of the bottom ends of the 6 active driving chains and the fixed platform form a circle, the intersections of the bottom ends of the 6 follow-up redundant measuring chains and the moving platform form a circle, and the two circles are concentric with the center O.

[0009] In the above-mentioned high-precision large-load redundant six-degree-of-freedom parallel mechanism, the active driving chain is an active motion unit and is driven by a servo motion module composed of a stepping motor, a reducer, and a lead screw guide rail.

[0010] In the above-mentioned high-precision large-load redundant six-degree-of-freedom parallel mechanism, the active driving chain controls the displacement with a pulse equivalent through an open-loop command, and the pulse equivalent is less than or equal to the resolution of the measuring element of the follow-up redundant measuring chain.

[0011] In the above-mentioned high-precision large-load redundant six-degree-of-freedom parallel mechanism, the pulse equivalent is the theoretical value of the displacement when the active driving chain receives a pulse command, and is obtained through the step angle of the stepping motor, the reduction ratio of the reducer, and the lead of the lead screw.

[0012] In the above-mentioned high-precision large-load redundant six-degree-of-freedom parallel mechanism, the follow-up redundant measuring chain is a follow-up measuring unit and does not impose constraints on the fixed platform and the moving platform.

[0013] In the above-mentioned high-precision and large-load redundant six-degree-of-freedom parallel mechanism, the follow-up redundant measurement branch chain is divided into two parts: a moving rod and a static rod; among them, the moving rod is connected to the upper platform through a spherical hinge, the static rod is connected to the lower platform through a spherical hinge, and there is only one translational degree of freedom between the moving rod and the static rod.

[0014] In the above-mentioned high-precision and large-load redundant six-degree-of-freedom parallel mechanism, the absolute grating scale reading heads are respectively fixed on the static rod and the moving rod through guide rails parallel to the axial direction of the follow-up redundant measurement branch chain; during pose adjustment, the active drive branch chain drives the upper platform to move, and the upper platform will also drive the measurement branch chain to follow, so that a relative displacement is generated between the reading head and the grating scale, the displacement change of the follow-up redundant measurement branch chain is measured, and the precise pose is solved in real time.

[0015] In the above-mentioned high-precision and large-load redundant six-degree-of-freedom parallel mechanism, the working process of the six-degree-of-freedom parallel mechanism is as follows:

[0016] Step 1: Establish the inverse kinematics mathematical model of the six-degree-of-freedom parallel mechanism and establish the Newton-Raphson forward kinematics mathematical model of the six-degree-of-freedom parallel mechanism;

[0017] Step 2: Determine the structural parameters r1, R1, α1, β1, r2, R2, α2, β2, H of the inverse kinematics mathematical model and the Newton-Raphson forward kinematics mathematical model;

[0018] Step 3: Measure the absolute positions of the upper and lower hinge points of the 6 follow-up redundant measurement branch chains through the grating scale;

[0019] Step 4: Substitute the absolute positions of the upper and lower hinge points of the 6 follow-up redundant measurement branch chains into the Newton-Raphson forward kinematics mathematical model to solve the pose of the moving platform at this time;

[0020] Step 5: Substitute the pose of the moving platform at this time into the inverse kinematics mathematical model to solve the actual positions of the 6 active drive branch chains at this time, which are used as the zero positions before pose adjustment;

[0021] Step 6: Input the target pose A of the moving platform;

[0022] Step 7: Substitute the target pose into the inverse kinematics mathematical model to calculate the displacement increments that the 6 active drive branch chains need to adjust;

[0023] Step 8: Call the servo motion module, convert the displacement increments of the 6 active drive branch chains into pulse numbers, and coordinately control the 6 active drive branch chains to move the moving platform to the target pose;

[0024] Step 9: Measure the positions of the 6 follow-up redundant measurement branch chains through the grating scale, substitute them into the Newton-Raphson forward kinematics mathematical model, and solve the current pose B of the moving platform.

[0025] Step Ten: Calculate the pose error e p , e p = A - B;

[0026] Step Eleven: Compare the pose error e p with the set error threshold. When e p is less than the error threshold, it is determined that the current pose adjustment is in place, and proceed to Step Twelve; otherwise, it is determined that the current pose adjustment is not in place, and return to Step Seven; until the adjustment is in place, then proceed to Step Twelve;

[0027] Step Twelve: Determine whether to continue with the next pose adjustment. If so, return to Step Six; otherwise, end.

[0028] In the above-mentioned high-precision large-load redundant six-degree-of-freedom parallel mechanism, in Step Two, r1 is the radius of the circle of the top hinge point of the active drive chain; R1 is the radius of the circle of the bottom hinge point of the active drive chain; α1 is half of the central angle of the short side of the top hinge point of the active drive chain; β1 is half of the central angle of the short side of the bottom hinge point of the active drive chain; r2 is the radius of the circle of the top hinge point of the follower redundant measurement chain; R2 is the radius of the circle of the bottom hinge point of the follower redundant measurement chain; α2 is half of the central angle of the short side of the top hinge point of the follower redundant measurement chain; β2 is half of the central angle of the short side of the bottom hinge point of the follower redundant measurement chain; H is the distance between the center p and the center O.

[0029] The beneficial effects of the present invention compared with the prior art are as follows:

[0030] (1) A high-precision large-load redundant six-degree-of-freedom parallel mechanism proposed by the present invention presents a design of six follower redundant measurement chains for precisely measuring the pose of a six-degree-of-freedom parallel mechanism with a load, overcoming the influence of large loads and large impact forces on the measurement accuracy of the active drive chains, and solving the problem of high-precision pose adjustment for large loads;

[0031] (2) A high-precision large-load redundant six-degree-of-freedom parallel mechanism proposed by the present invention presents a pose closed-loop control method that uses follower redundant measurement chains to precisely measure the position of the redundant chains and then solve the pose, solving the problem of pose closed-loop control for parallel mechanisms;

[0032] (3) In the present invention, the active drive chains are active motion units for realizing various pose adjustment motions of the parallel mechanism; the follower redundant measurement chains are precision measurement units. The layout of their upper and lower hinge points makes them immune to the impact forces of large loads and does not restrict any degree of freedom of the platform. They only follow and precisely measure the distance between the upper and lower hinge points of the redundant hinges, and apply the forward kinematic solution to obtain the precise pose of the six-degree-of-freedom parallel mechanism, which is applied to the precise adjustment of the main mirror or secondary mirror with a large load in large-aperture optics, and has strong engineering application value. Description of the Drawings

[0033] Figure 1 Schematic diagram of the six-degree-of-freedom parallel mechanism of the present invention;

[0034] Figure 2 This is a schematic diagram of the hinge point distribution of the dynamic platform of the present invention;

[0035] Figure 3 This is a schematic diagram of the hinge point distribution of the static platform of the present invention;

[0036] Figure 4 It is composed of the six-degree-of-freedom parallel mechanism control system of the present invention;

[0037] Figure 5 This is a control flow chart of the six-degree-of-freedom parallel mechanism of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further described below with reference to the embodiments.

[0039] The present invention provides a high-precision, large-load, redundant six-degree-of-freedom parallel mechanism. The large load generates a large interference force in different postures, causing the active drive branch of the parallel mechanism to be significantly impacted during operation. The active drive branch will deform, making it impossible to accurately measure the length of the active drive branch using the traditional method of directly measuring the length of the active drive branch using a linear measuring element. That is, the deformation of the active drive branch will affect its measurement accuracy. The posture control of the six-degree-of-freedom parallel mechanism depends on the measurement accuracy of the position of the active drive branch, which affects the posture control accuracy of the six-degree-of-freedom parallel mechanism. In order to overcome the influence of large loads and large impact forces on the measurement accuracy of the active drive branch, a redundant six-degree-of-freedom parallel mechanism with a measurement branch separated from the active drive branch is proposed, comprising a fixed platform, a moving platform, six active drive branches, six follower redundant measurement branches, and a controller. The fixed platform and the moving platform are connected by six groups of identical active drive branches and six groups of follower redundant measurement branches. The active drive branch is the active motion unit, responsible for achieving various posture adjustment motions of the parallel mechanism. The follower redundant measurement branch is a precision measurement unit. The layout of its upper and lower hinges protects it from the impact of large loads and does not constrain any degrees of freedom of the platform. It only accurately measures the distance between the upper and lower hinges of the redundant hinges, applying the kinematic solution to determine the precise posture of the six-degree-of-freedom parallel mechanism. A controller executes the closed-loop posture control algorithm for the redundant six-degree-of-freedom parallel mechanism, achieving precise posture control. This redundant six-degree-of-freedom parallel mechanism design improves the high-load motion accuracy of the parallel mechanism and can be applied to the precision adjustment of high-load primary or secondary mirrors in large-aperture optics, demonstrating its strong engineering application value.

[0040] Six-degree-of-freedom parallel mechanism, such as Figure 1As shown in the figure, it includes a fixed platform, a moving platform, six active drive branches, and six follow-up redundant measurement branches. Among them, the fixed platform is a horizontally placed frustum structure; the moving platform is horizontally and coaxially arranged above the fixed platform; the six active drive branches are arranged between the fixed platform and the moving platform, connecting the fixed platform and the moving platform; the bottom ends of the six active drive branches are circumferentially distributed along the fixed platform; the top ends of the six active drive branches are circumferentially distributed along the moving platform; the six follow-up redundant measurement branches are arranged between the fixed platform and the moving platform, connecting the fixed platform and the moving platform; the bottom ends of the six follow-up redundant measurement branches are circumferentially distributed along the fixed platform; the top ends of the six follow-up redundant measurement branches are circumferentially distributed along the moving platform; the six active drive branches are located on the circumferential outer side of the six follow-up redundant measurement branches; the top end of the active drive branch is connected to the moving platform through a hinge, and the bottom end of the active drive branch is connected to the fixed platform through a hinge; the top end of the follow-up redundant measurement branch is connected to the moving platform through a spherical hinge, and the bottom end of the follow-up redundant measurement branch is connected to the fixed platform through a spherical hinge.

[0041] The intersections of the top ends of the six active drive branches and the moving platform form a circle, and the intersections of the top ends of the six follow-up redundant measurement branches and the moving platform form a circle. The two circles are concentric, and the center is p; the intersections of the bottom ends of the six active drive branches and the fixed platform form a circle, and the intersections of the bottom ends of the six follow-up redundant measurement branches and the moving platform form a circle. The two circles are concentric, and the center is O.

[0042] The active drive branch is an active motion unit, which is driven by a servo motion module composed of a stepping motor, a reducer, and a lead screw guide rail. The active drive branch controls the displacement with a pulse equivalent through an open-loop command, and its pulse equivalent is less than or equal to the resolution of the measurement element of the follow-up redundant measurement branch. The pulse equivalent is the theoretical value of the displacement when the active drive branch receives a pulse command, and it is obtained through the step angle of the stepping motor, the reduction ratio of the reducer, and the lead of the lead screw.

[0043] The follow-up redundant measurement branch is a follow-up measurement unit, which does not generate constraints on the fixed platform and the moving platform. The follow-up redundant measurement branch is divided into two parts: a moving rod and a static rod. Among them, the moving rod is connected to the upper platform through a ball hinge, and the static rod is connected to the lower platform through a ball hinge. There is only one translational degree of freedom between the moving rod and the static rod. The absolute grating scale reading head is fixed to the static rod and the moving rod respectively through a guide rail parallel to the axis of the follow-up redundant measurement branch. During pose adjustment, the active drive branch drives the upper platform to move, and the upper platform will also drive the measurement branch to follow. As a result, a relative displacement is generated between the reading head and the grating scale, and the displacement change of the follow-up redundant measurement branch is measured, and the accurate pose is solved in real time.

[0044] The working process of the six-degree-of-freedom parallel mechanism is as follows:

[0045] Step 1: Establish the inverse kinematics mathematical model of the six-degree-of-freedom parallel mechanism and the Newton-Raphson forward kinematics mathematical model of the six-degree-of-freedom parallel mechanism.

[0046] Step 2: Determine the structural parameters r1, R1, α1, β1, r2, R2, α2, β2, H of the inverse kinematics mathematical model and the Newton-Raphson forward kinematics mathematical model; r1 is the radius of the circle of the top hinge point of the active drive chain; R1 is the radius of the circle of the bottom hinge point of the active drive chain; α1 is half of the central angle of the short side of the top hinge point of the active drive chain; β1 is half of the central angle of the short side of the bottom hinge point of the active drive chain; r2 is the radius of the circle of the top hinge point of the follower redundant measurement chain; R2 is the radius of the circle of the bottom hinge point of the follower redundant measurement chain; α2 is half of the central angle of the short side of the top hinge point of the follower redundant measurement chain; β2 is half of the central angle of the short side of the bottom hinge point of the follower redundant measurement chain; H is the distance between the center p and the center O.

[0047] Step 3: Measure the absolute positions of the upper and lower hinge points of the 6 follower redundant measurement chains through the grating ruler.

[0048] Step 4: Substitute the absolute positions of the upper and lower hinge points of the 6 follower redundant measurement chains into the Newton-Raphson forward kinematics mathematical model to calculate the pose of the moving platform at this time.

[0049] Step 5: Substitute the pose of the moving platform at this time into the inverse kinematics mathematical model to calculate the actual positions of the 6 active drive chains at this time, which are used as the zero positions before pose adjustment.

[0050] Step 6: Input the target pose A of the moving platform.

[0051] Step 7: Substitute the target pose into the inverse kinematics mathematical model to calculate the displacement increments that the 6 active drive chains need to adjust.

[0052] Step 8: Call the servo motion module, convert the displacement increments of the 6 active drive chains into pulse numbers, and coordinately control the coordinated movement of the 6 active drive chains to move the moving platform to the target pose.

[0053] Step 9: Measure the positions of the 6 follower redundant measurement chains through the grating ruler, substitute them into the Newton-Raphson forward kinematics mathematical model, and calculate the current pose B of the moving platform.

[0054] Step 10: Calculate the pose error e p , e p = A - B.

[0055] Step 11: Compare the pose error e p with the set error threshold. When e pWhen it is less than the error threshold, it is determined that the current pose adjustment is in place, and step twelve is entered; otherwise, it is determined that the current pose adjustment is not in place, and step seven is returned; until the adjustment is in place, step twelve is entered.

[0056] Step twelve: Determine whether to continue with the next pose adjustment. If necessary, return to step six; otherwise, end.

[0057] A high-precision large-load redundant six-degree-of-freedom parallel mechanism of the present invention is as Figure 2 shown. The redundant six-degree-of-freedom parallel mechanism includes a fixed platform, a moving platform, six active drive branches, six follow-up redundant measurement branches, and a controller. The fixed platform and the moving platform are connected by six groups of identical active drive branches and six groups of identical follow-up redundant measurement branches. The six active drive branches are active motion units for realizing various pose adjustment motions of the mechanism; the six follow-up redundant measurement branches are precision measurement units. The layout of their upper and lower hinge points makes them immune to large-load impact forces. The six follow-up redundant measurement branches only follow and are responsible for accurately measuring the distance between the rotation centers of the upper and lower hinges of the redundant branches, that is, the hinge points, and substituting it into the forward kinematic model of the parallel mechanism to calculate the accurate pose of the six-degree-of-freedom parallel mechanism. The controller is used to execute the pose closed-loop control algorithm of the redundant six-degree-of-freedom parallel mechanism to achieve precise adjustment of the pose.

[0058] The six active drive branches are active motion units, which can be composed of a stepper motor + a reducer + a lead screw guide rail. The active drive branches have no linear measurement elements, but the displacement can be controlled by an open-loop command with a pulse equivalent, and the pulse equivalent is less than or equal to the resolution of the measurement elements of the measurement branches. For example, if the measurement element of the follow-up redundant measurement branch is a grating scale with a resolution of 10 nm, the pulse equivalent of the active drive branch should be less than 10 nm. The pulse equivalent is the theoretical value of the displacement when the active drive branch receives a pulse command, and can be obtained through the step angle of the stepper motor, the reduction ratio of the reducer, and the lead of the lead screw.

[0059] The six follow-up redundant measurement branches can adopt a spherical hinge - translational pair - spherical hinge (SPS) structure. The measurement branches do not freely generate constraints on the upper and lower platforms and belong to follow-up measurement units. The measurement branches are divided into a moving rod and a static rod. The moving rod is connected to the upper platform through a spherical hinge, and the static rod is connected to the lower platform through a spherical hinge. There is a translational degree of freedom between the moving and static rods. The absolute grating scale and its reading head are respectively fixed to the static rod and the moving rod through a guide rail parallel to the axis. In this way, when the pose is adjusted, the active drive branch drives the upper platform to move, and at the same time drives the measurement branch to follow. The reading head and the grating scale generate a relative displacement, thereby outputting the displacement change of the measurement branch. Since the layout of the upper and lower hinge points of the measurement branch is in the non-load-bearing area of the upper platform, it is immune to the influence of large-load impact forces, and the absolute grating scale has high precision, so the distance between the upper and lower hinge points of the redundant hinge can be accurately measured in real time for real-time accurate pose calculation.

[0060] Step 1: Determine the structural parameters r1, R1, α1, β1, H of the active driving branch active six-degree-of-freedom parallel mechanism and the structural parameters r2, R2, α2, β2 of the follower redundant measurement branch follower measurement six-degree-of-freedom parallel mechanism; according to factors such as the load diameter, weight, and working space of the redundant six-degree-of-freedom parallel mechanism, determine its envelope space, and within this envelope space range, layout the upper and lower hinge points of the active driving branch and the redundant measurement branch. The coordinate system and hinge point layout are as Figure 1 , Figure 2 , Figure 3 shown.

[0061] As Figure 1 shown, the six-degree-of-freedom parallel mechanism is simplified to a static platform, a moving platform, 6 active driving branches (each active driving branch has a moving rod and a static rod) and their 6 upper hinges and 6 lower hinges; 6 follower measurement branches (each follower measurement branch has a moving rod and a static rod) and their 6 upper hinges and 6 lower hinges. The structural parameters of the active driving branch six-degree-of-freedom parallel mechanism are r1 (the radius of the hinge point circle of the moving rod of the active driving branch), R1 (the radius of the hinge point circle of the static rod of the active driving branch), α1 (half of the central angle of the short side of the hinge point of the moving rod of the active driving branch), β1 (half of the central angle of the short side of the hinge point of the static rod of the active driving branch), and H (the distance between p and O at the zero position of the parallel mechanism). The structural parameters of the follower measurement branch six-degree-of-freedom parallel mechanism are r2 (the radius of the hinge point circle of the moving rod of the follower measurement branch), R2 (the radius of the hinge point circle of the static rod of the follower measurement branch), α2 (half of the central angle of the short side of the hinge point of the moving rod of the follower measurement branch), β2 (half of the central angle of the short side of the hinge point of the static rod of the follower measurement branch). Determining the above parameters can completely describe the basic structure of the active six-degree-of-freedom parallel mechanism. In order to quantitatively represent the coordinates of each point on the upper platform, a static coordinate system O-XYZ is established at the center of the circle where the lower platform hinge points are located, with the coordinate origin being O; a moving coordinate system p-xyz is established at the center of the circle where the upper platform hinge points are located, with the coordinate origin being p, and the directions of each coordinate system are as Figure 1 shown.

[0062] Establish the mathematical model of the inverse kinematics solution:

[0063] The kinematic analysis of the parallel mechanism is the basis for dynamic analysis, control strategy research, and structural optimization design. Therefore, establishing an accurate kinematic model is crucial for the research of the parallel mechanism. The structure of the large-load redundant six-degree-of-freedom parallel mechanism is as Figure 1As shown, the active drive branch chain and the platform are connected by hinges A1, A2, A3, A4, A5, A6 and hinges B1, B2, B3, B4, B5, B6. The follower measurement branch chain and the platform are connected by hinges A1’, A2’, A3’, A4’, A5’, A6’ and hinges B1’, B2’, B3’, B4’, B5’, B6’. The lower platform is used as the static platform. Taking the displacement of the active drive branch chain as the input variable, the spatial displacement and attitude of the moving platform (upper platform) can be controlled. In the actual mechanism, the movement of the moving platform of the parallel mechanism is realized by changing the lengths of the six retractable active drive branch chains, that is, the translation along the x, y, and z axes and the Euler angles U, V, and W of rotation around the x, y, and z axes of the moving coordinate system. In the present invention, the rotation is selected in the order of the moving coordinate system z→y→x coordinate axes, which is the same as the result of rotating three times around the fixed axes of the static coordinate system in the opposite order. After three rotations, the final rotation transformation matrix shown in Equation (1) can be obtained It is used to convert the pose of the moving coordinate system into the static coordinate system, that is, to unify the coordinates of each point of the moving platform in the static coordinate system, calculate the position of the active drive branch chain (kinematic inverse solution) according to the target pose of the moving platform, or calculate the current pose of the moving platform (kinematic forward solution) according to the position of the branch chain;

[0064]

[0065] Among them, cU = cos(U), cV = cos(V), cW = cos(W), sU = sin(U), sV = sin(V), sW = sin(W). The generalized coordinate vector q of the attitude of the moving platform is q = [x y z U V W] T When, the lengths of the active drive branch chains are shown in Equation (2):

[0066]

[0067] Among them, the vector l i is Figure 1 the branch chain vector A shown i B i l i is the branch chain length, i = 1, 2,..., 6, and i represents the serial number of the active drive branch chain. So far, the mathematical model of the kinematic inverse solution of the parallel mechanism has been established.

[0068] Establish the mathematical model of the kinematic forward solution:

[0069] The present invention applies the Newton-Raphson method to solve the kinematic forward solution of the six-degree-of-freedom parallel mechanism.

[0070] Define the following target vector function f to describe the estimated value l of the telescopic length of the active drive branch chain i measured value The differences between them are as follows:

[0071]

[0072] In formula (3), f1……f6 respectively represent the estimated values l of the telescopic lengths of 6 branched chains i of the square and the measured value of the square.

[0073] The steps for solving the pose array Q of the six-degree-of-freedom parallel mechanism by the Newton-Raphson method with the objective of minimizing the target vector function f are as follows:

[0074] 1), Measure the coordinate vectors of 6 active driving branched chains Select the initial pose value Q of the moving platform;

[0075] 2), Based on the initial pose value Q of the moving platform and using the inverse solution formula, calculate the lengths l of each active driving branched chain;

[0076] 3), Based on the coordinate vectors of 6 active driving branched chains and the lengths l of the active driving branched chains, form the array function f;

[0077] 4), Calculate the Jacobian matrix

[0078] 5), Use JδQ = -f to calculate the pose correction value δQ;

[0079] 6), If δQ T δQ < ε (ε is the pose error threshold) holds, then Q is the required pose, otherwise, go to the next step;

[0080] 7), Calculate Q = Q + δQ, and go back to step 2).

[0081] The calculation formula of the Jacobian matrix in step 4) is as follows:

[0082]

[0083] In the formula,

[0084] J i1 = 2l ix

[0085] J i2 = 2l iy

[0086] J i3 = 2l iz

[0087]

[0088] Ji5 = 2(R row3 p b i (l ix cos W + l iy sin U) - l iz ( p b ix cosV + p b iy sin V sin U + p b iz sinV cos U))

[0089] J i6 = 2(l iy R row1 p b i - l ix R row2 p b i )

[0090] l i = [l ix l iy l iz ) T is the coordinate vector of the i-th active driving branch chain;

[0091] p b i = p b ix p b iy p b iz is the coordinate vector of the hinge point corresponding to the i-th active driving branch chain on the moving platform in the moving coordinate system p-xyz coordinate system;

[0092] represents the second column of the rotation transformation matrix ;

[0093] represents the third column of the rotation transformation matrix ;;

[0094] R row1 = [cWcU cWsVsU - sWcU cWsVcU + sWsU], represents the first row of the rotation transformation matrix ; R row2 = [sWcV sWsVsU + cWcU sWsVcU - cWsU], represents the second row of the rotation transformation matrix ; R row3= [-sV cVsUcVcU], representing the rotation transformation matrix of the third row.

[0095] Step 2: Establish a parametric virtual prototype model of the redundant six-degree-of-freedom parallel mechanism in ADAMS;

[0096] ADAMS (Automatic Dynamic Analysis of Mechanical System) is a software for dynamic analysis of mechanical systems, a product of MSC Corporation in the United States. It combines the multi-body dynamics modeling method with the functions of large-displacement and non-linear analysis and solution. Using this software, a complex multi-body dynamics virtual prototype model can be created conveniently and quickly. Then, forces / moments or other motion excitations are applied to the geometric model. Finally, a simulation test similar to the actual motion condition is performed, and the required measurement values such as position, force / moment, velocity, and acceleration are output. It can know how the prototypes of various design schemes work long before the physical prototype is built. The ADAMS / View interface module is a user-centered interactive graphic environment. It provides a rich library of part geometric graphics, constraint libraries, and force libraries, integrating convenient icon operations, menu operations, mouse-click operations with functions such as interactive graphic modeling, simulation calculation, animation display, optimization design, X-Y curve graph processing, result analysis, and data printing. In the part library it provides, objects of various basic shapes can be created.

[0097] When usually modeling with ADAMS software, the built-in geometric body module is used for modeling. After determining the parameters of the geometric body, the geometric body is also determined. When the size of the geometric body changes or it is necessary to analyze the influence of parameters on the entire system, the parameters need to be modified manually, which greatly increases the workload. To avoid repetitive work, ADAMS provides a parametric modeling function, representing the characteristic values of the established model with design parameters set in ADAMS. In this way, when modifying the model, only the design parameters need to be modified, and the model can change accordingly. Especially when performing parameter analysis in ADAMS, by averaging the design parameters within the set interval, the model can be automatically updated, and ADAMS automatically performs a series of simulations to facilitate observing the changes in the performance of the prototype under different parameter values, which greatly simplifies the manual modification process. After opening the ADAMS software and setting up the working environment of ADAMS, design variables can be defined. The model of the large-load redundant six-degree-of-freedom parallel mechanism of the present invention is established under ADAMS / View. The entire parallel mechanism system is simplified into a static platform, i.e., the lower platform, a moving platform, i.e., the upper platform, 6 active driving chains and their 12 Hooke hinges, 6 follower measurement hinges and their 12 ball hinges. The parametric virtual prototype model in ADAMS is as Figure 2 shown.

[0098] Step 3: Kinematic and dynamic simulation to analyze the kinematic and dynamic performance of the redundant six-degree-of-freedom parallel mechanism;

[0099] After the model is built, the ADAMS / Solver module automatically generates the dynamic equations of the mechanical system model and presents the solutions of statics, kinematics, and dynamics. The ADAMS / Postprocessor module can be used to output high-performance animations, various data curves, and can also perform operations such as integration, differentiation, summation, and subtraction on the curves. These two modules can be used to perform simulation analysis on the kinematics and dynamics of the parallel mechanism.

[0100] Kinematic analysis

[0101] When the moving platform of the redundant six-degree-of-freedom parallel mechanism performs pose adjustment movement, its speed and acceleration have a strict dependence relationship with the speed and acceleration of the telescoping of each rod, but the relationship between the length of the active drive link and the pose of the moving platform is non-linear. In order to realize the movement of the 6 degrees of freedom of the moving platform of the redundant six-degree-of-freedom parallel mechanism virtual prototype in ADAMS, a general point motion excitation is applied at the center of the moving platform to achieve its motion simulation, so that the moving platform realizes the movement along the x, y, and z axes and the rotation around the X, Y, and Z axes, so as to simulate the general movement of the moving platform in actual work.

[0102] Through kinematic analysis, the stroke ranges of the corresponding active drive links and the follower redundant measurement links of the working space of the redundant six-degree-of-freedom parallel mechanism, the rotation angle ranges of the upper and lower hinges, and the pose resolution corresponding to the active drive links and the six follower redundant measurement links can be obtained.

[0103] Dynamic analysis

[0104] For the given driving force or torque of each active drive link, the pose change and dynamic movement process of the redundant six-degree-of-freedom parallel mechanism not only depend on its geometric structure, but also rely on the inertia, that is, the mass of each active drive link. For the redundant six-degree-of-freedom parallel mechanism, when the moving platform realizes a certain movement under a certain load, the driving force of each active drive link will also change accordingly. Whether the change of the driving force of each active drive link during the movement process is smooth and whether the magnitude of the force meets the requirements are of great significance for the design of the mechanism, the selection of servo actuators, and the actual control. This requires dynamic analysis.

[0105] The dynamic analysis of a redundant six-degree-of-freedom parallel mechanism includes aspects such as the dynamic modeling of the mechanism, force analysis, calculation of inertial forces, dynamic balance, and dynamic response. It plays a very important role in the design and control of a redundant six-degree-of-freedom parallel mechanism and is the basis for determining the main structural parameters of the redundant six-degree-of-freedom parallel mechanism. Due to the complexity of the redundant six-degree-of-freedom parallel mechanism, its dynamic model is usually a complex system with multiple degrees of freedom, multiple variables, highly nonlinear, and multi-parameter coupling. When using ADAMS to simulate the dynamics of a parallel mechanism, ADAMS will automatically establish the Lagrangian motion equations of the system according to the mechanical system model, list the Lagrangian equations with multipliers for six generalized coordinates and the corresponding constraint equations for each rigid body, and automatically solve them without the need for users to program and calculate.

[0106] When performing dynamic analysis, it is necessary to know the output force of each drive branch chain of the moving platform of the redundant six-degree-of-freedom parallel mechanism at any pose. The output force of the active drive branch chain can be obtained by performing a forward kinematic solution of the redundant six-degree-of-freedom parallel mechanism.

[0107] Step 4, design the active drive branch chain and the follow-up redundant measurement branch chain according to the simulation results;

[0108] According to the analysis results of the branch chain stroke in the kinematic analysis results of Step 3, design the strokes of both the active drive branch chain and the measurement branch chain to be 1.5 to 2 times the maximum value of the analysis results. While ensuring the pose workspace of the redundant six-degree-of-freedom parallel mechanism, it also leaves a margin for safety limit and so on.

[0109] According to the dynamic analysis results, analyze the torque required for the active drive branch chain according to the maximum force received by the active drive branch chain at the pose with the maximum load and the most severe conditions, and select the motor and design the reducer with a margin of 1.5 to 2 times this maximum torque.

[0110] According to the resolution requirements of the drive branch chain required for the pose resolution of the redundant six-degree-of-freedom parallel mechanism analyzed in Step 3, the designed reducer should meet the resolution requirements of the active drive branch chain. [[ID=1……]]

[0111] Step 5, design the controller of the redundant six-degree-of-freedom parallel mechanism according to the motor and absolute encoder selected in Step 4; The control system of the redundant six-degree-of-freedom parallel mechanism is composed as Figure 4 shown, and consists of three major parts: the upper computer controller, the lower computer controller, and the execution and feedback components of the redundant six-degree-of-freedom parallel mechanism. The upper computer can be an ordinary PC, and the lower computer can be multiple PCI boards inserted into the PC chassis, communicating with the host through the PCI bus. Of course, the lower computer can also be a circuit board independent of the PC, communicating with the upper computer through the RS232 serial port or network port.

[0112] The host computer control module mainly includes a human-machine interface module, an inverse kinematics module, a forward kinematics module, a pose simulation display module, and a communication module with the lower computer. The human-machine interface module is responsible for the input of instructions and the display of real-time pose and position; the inverse kinematics module is responsible for solving the target pose into the positions of the active drive branches; the forward kinematics module is responsible for calculating the pose of the redundant six-degree-of-freedom parallel mechanism in real time according to the positions of the follow-up redundant measurement branches; the pose simulation display module is responsible for generating and displaying the motion state and pose of the redundant six-degree-of-freedom parallel mechanism in the form of data and graphics on the host computer human-machine interface; the communication module with the lower computer is responsible for sending instructions and receiving motion state data from the lower computer through the PCI bus or other communication protocols.

[0113] The lower computer control module includes a control circuit board based on DSP+FPGA. Among them, DSP is responsible for the inverse solution module, servo algorithm, and forward solution module, and FPGA is responsible for the real-time acquisition of position feedback data of the follow-up measurement branches. The inverse solution module calculates the displacement increments of each active drive branch according to the target pose and the current pose to form servo control instructions; the servo module drives the motors of each branch to execute motion according to the displacement increments of the active drive branches calculated by the inverse solution module in the servo cycle. The displacement amount in each servo cycle determines the speed of the active drive branches; the forward solution module calculates the current pose according to the positions of the follow-up redundant measurement branches collected by FPGA in real time. The drive circuit board is responsible for executing the instructions issued by the servo algorithm module, converting the instructions into square waves with a certain frequency and a certain number, and driving each active drive branch to move to the target position coordinately at an appropriate speed.

[0114] The six-degree-of-freedom parallel mechanism part includes the actuators of the active drive branches 1-6: stepper motors, reducers, lead screws, and limit switches; the measuring elements of the follow-up redundant measurement branches 1-6: absolute grating rulers and limit switches. The stepper motor is responsible for executing the drive signal of the drive circuit board, and the displacement of the active drive branch forms the pose output of the upper platform of the redundant six-degree-of-freedom parallel mechanism; the absolute grating ruler records the linear displacement of the follow-up redundant measurement branch in real time, sends the branch position data to the FPGA of the control circuit board, forms a position closed loop, and further forms a pose closed loop of the parallel mechanism. During the movement of the parallel mechanism, FPGA monitors the limit signal in real time. After the limit switch is triggered, a stop instruction is directly sent to avoid overrun.

[0115] Step 6, control flow;

[0116] Its control implementation is jointly realized by the host computer human-machine interface and the lower computer DSP and FPGA software. The operator only needs to input the target pose or stop the program on the human-machine interface, and the rest are automatically realized by the software. The control flow is as Figure 5 shown, including the following steps:

[0117] Step 1: Establish the kinematic model of the six-degree-of-freedom parallel mechanism, including establishing the inverse kinematic mathematical model and the forward kinematic mathematical model of the six-degree-of-freedom parallel mechanism;

[0118] Step 2: Parameter initialization, including structural parameters r1, R1, α1, β1, r2, R2, α2, β2, H;

[0119] Step 3: Read the absolute positions of the upper and lower hinge points of the six measurement branches;

[0120] Step 4: Call the forward kinematic module to calculate the pose at this time;

[0121] Step 5: Call the inverse kinematic module to calculate the actual positions of the active drive branches at this time, and memorize these positions as the zero positions of the active drive branches for this pose adjustment;

[0122] Step 6: Input the target pose;

[0123] Step 7: Call the inverse kinematic module to calculate the required displacement increments of the active drive branches;

[0124] Step 8: Call the servo motion module to convert the displacement increments of the active drive branches into pulse numbers, and coordinately control the six active drive branches to move to the command position at a suitable speed;

[0125] Step 9: The six follower redundant measurement branches perform follow-up measurements, and call the forward kinematics to calculate the pose when in place;

[0126] Step 10: Calculate the pose error, e p = target pose - current pose difference;

[0127] Step 11: Determine whether the pose error is less than the threshold. If it is less than the threshold, the current pose adjustment is in place, and go to Step 12; otherwise, go to Step 7 to continue adjusting the pose;

[0128] Step 12: Determine whether to continue the next pose adjustment. If necessary, go to Step 6; otherwise, end.

[0129] Among them, the relatively key steps include:

[0130] Step 4 and Step 9: Read the absolute positions of the upper and lower hinge points of the six follower redundant measurement branches; call the forward kinematic module to calculate the pose at this time;

[0131] The real-time positions of the six follower redundant measurement branches will be collected by the FPGA. By calling the forward kinematic module, that is, the aforementioned formulas (3) and (4), the current pose can be calculated in real time.

[0132] Steps 5 and 7: Call the inverse kinematics module to calculate the actual positions of the six active drive branches at this time, and memorize these positions as the zero positions of the active drive branches for this pose adjustment.

[0133] In this step, according to the initial pose at initialization, call the inverse kinematics module, that is, the aforementioned formulas (1) and (2), to calculate the actual positions of the six active drive branches of the current pose. Especially in step 5, since the active drive branches have no absolute zero position, this position is memorized as the zero position after power-on.

[0134] Step 8: Call the servo motion module to convert the displacement increments of the active drive branches into pulse numbers and pulse frequencies, and coordinately control the six active drive branches to move to the command position at an appropriate speed in a coordinated manner.

[0135] From the perspective of servo control, the motion space of the moving platform is the virtual axis space, while the drive joint space is the real axis space. Therefore, during motion control, it is necessary to use the inverse position model to transform the given pose and speed information of the moving platform into control commands for the rod lengths of each rod of the servo system, so as to drive the moving platform of the parallel mechanism to achieve the desired motion.

[0136] Input the control quantities of each active drive branch into the servo module. The servo module will drive each branch to move at different speeds according to the servo cycle to achieve the coordinated and precise motion of each active drive branch.

[0137] Although the present invention has been disclosed above with preferred embodiments, it is not used to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by using the disclosed methods and technical contents without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change, and modification made to the above embodiments according to the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A high-precision large-load redundant six-degree-of-freedom parallel mechanism, characterized in that: It includes a fixed platform, a moving platform, six active driving linkages, and six follow-up redundant measurement linkages; among them, the fixed platform is a horizontally placed frustum structure; the moving platform is horizontally and coaxially arranged above the fixed platform; the six active driving linkages are arranged between the fixed platform and the moving platform, connecting the fixed platform and the moving platform; the bottoms of the six active driving linkages are circumferentially distributed along the fixed platform; the tops of the six active driving linkages are circumferentially distributed along the moving platform; the six follow-up redundant measurement linkages are arranged between the fixed platform and the moving platform, connecting the fixed platform and the moving platform; the bottoms of the six follow-up redundant measurement linkages are circumferentially distributed along the fixed platform; the tops of the six follow-up redundant measurement linkages are circumferentially distributed along the moving platform; the six active driving linkages are located on the circumferential outer side of the six follow-up redundant measurement linkages; the top of the active driving linkage is connected to the moving platform through a hinge, and the bottom of the active driving linkage is connected to the fixed platform through a hinge; the top of the follow-up redundant measurement linkage is connected to the moving platform through a spherical hinge, and the bottom of the follow-up redundant measurement linkage is connected to the fixed platform through a spherical hinge; The follow-up redundant measurement linkage is a follow-up measurement unit and does not impose constraints on the fixed platform and the moving platform; The follow-up redundant measurement linkage is divided into two parts: a moving rod and a static rod; among them, the moving rod is connected to the upper platform through a ball hinge, the static rod is connected to the lower platform through a ball hinge, and there is only one translational degree of freedom between the moving rod and the static rod; The absolute grating scale reading head is respectively fixed on the static rod and the moving rod through a guide rail parallel to the axis of the follow-up redundant measurement linkage; during pose adjustment, the active driving linkage drives the upper platform to move, and the upper platform will also drive the measurement linkage to follow, so that a relative displacement is generated between the reading head and the grating scale, and the displacement change of the follow-up redundant measurement linkage is measured, and the precise pose solution is carried out in real time.

2. The high-precision large-load redundant six-degree-of-freedom parallel mechanism according to claim 1, characterized in that: The intersections of the tops of the six active driving linkages and the moving platform form a circle, the intersections of the tops of the six follow-up redundant measurement linkages and the moving platform form a circle, the two circles are concentric, and the center of the circle is p; the intersections of the bottoms of the six active driving linkages and the fixed platform form a circle, the intersections of the bottoms of the six follow-up redundant measurement linkages and the moving platform form a circle, the two circles are concentric, and the center of the circle is O.

3. A high-precision large-load redundant six-degree-of-freedom parallel mechanism according to claim 2, characterized in that: The active driving linkage is an active motion unit and is driven by a servo motion module composed of a stepping motor, a reducer, and a lead screw guide rail.

4. A high-precision and large-load redundant six-degree-of-freedom parallel mechanism according to claim 3, characterized in that: The active driving linkage controls the displacement with a pulse equivalent through an open-loop command, and its pulse equivalent is less than or equal to the resolution of the measuring element of the follow-up redundant measurement linkage.

5. A high-precision large-load redundant six-degree-of-freedom parallel mechanism according to claim 4, characterized in that: The pulse equivalent is the theoretical value of the displacement when the active driving linkage receives a pulse command, and is obtained through the step angle of the stepping motor, the reduction ratio of the reducer, and the lead of the lead screw.

6. The high-precision large-load redundant six-degree-of-freedom parallel mechanism according to claim 5, characterized in that: The working process of the six-degree-of-freedom parallel mechanism is as follows: Step 1: Establish a mathematical model for the inverse kinematics solution of the six-degree-of-freedom parallel mechanism and establish a Newton-Raphson forward kinematics mathematical model for the six-degree-of-freedom parallel mechanism; Step 2: Determine the structural parameters r1, R1, α1, β1, r2, R2, α2, β2, H of the inverse kinematics mathematical model and the Newton-Raphson forward kinematics mathematical model; r1 is the radius of the circle of the top hinge point of the active driving link; R1 is the radius of the circle of the bottom hinge point of the active driving link; α1 is half of the central angle of the short side of the top hinge point of the active driving link; β1 is half of the central angle of the short side of the bottom hinge point of the active driving link; r2 is the radius of the circle of the top hinge point of the follower redundant measurement link; R2 is the radius of the circle of the bottom hinge point of the follower redundant measurement link; α2 is half of the central angle of the short side of the top hinge point of the follower redundant measurement link; β2 is half of the central angle of the short side of the bottom hinge point of the follower redundant measurement link; H is the distance between the center p and the center O. Step 3: Measure the absolute positions of the upper and lower hinge points of the 6 follower redundant measurement links through the grating ruler; Step 4: Substitute the absolute positions of the upper and lower hinge points of the 6 follower redundant measurement links into the Newton-Raphson forward kinematics mathematical model to calculate the pose of the moving platform at this time; Step 5: Substitute the pose of the moving platform at this time into the inverse kinematics mathematical model to calculate the actual positions of the 6 active driving links at this time, which are used as the zero positions before pose adjustment; Step 6: Input the target pose A of the moving platform; Step 7: Substitute the target pose into the inverse kinematics mathematical model to calculate the displacement increments that the 6 active driving links need to adjust; Step 8: Call the servo motion module, convert the displacement increments of the 6 active driving links into pulse numbers, and coordinately control the coordinated movement of the 6 active driving links to move the moving platform to the target pose; Step 9: Measure the positions of the 6 follower redundant measurement links through the grating ruler, substitute them into the Newton-Raphson forward kinematics mathematical model, and calculate the current pose B of the moving platform; Step Ten: Calculate the pose error e p , e p = A - B; Step Eleven: Compare the pose error e p with the set error threshold. When e p is less than the error threshold, it is determined that the current pose adjustment is in place, and proceed to Step Twelve; otherwise, it is determined that the current pose adjustment is not in place, and return to Step Seven; until the adjustment is in place, then proceed to Step Twelve; Step 12: Determine whether to continue the next pose adjustment. If necessary, return to Step 6; otherwise, end.

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