A design method of asymmetric S-shaped displacement curve for high-speed mechanism

Abstract

The application discloses a kind of asymmetric S-shaped displacement curve design methods suitable for high-speed mechanism, belong to displacement curve design technical field, the method includes: time segmentation is carried out to curve;Acceleration curve on time domain universe is constructed, and acceleration segmented function is obtained;Velocity segmented function and displacement segmented function are obtained by integration in turn;When the difference between the maximum displacement of current calculation and the target displacement maximum value of design is less than the maximum displacement error allowed, the product of acceleration and velocity is calculated, and the maximum value of absolute value is solved;After optimization for many times, the minimum of the maximum value of absolute value of the product of acceleration and velocity is selected, and the corresponding displacement segmented function is obtained;The dimensionless processing is carried out to displacement segmented function.The application can realize fast acceleration in curve starting section, and can eliminate the mutation of force in high-speed mechanism.

Description

Technical Field

[0001] This invention relates to the field of displacement curve design technology, and in particular to an asymmetric S-shaped displacement curve design method suitable for high-speed mechanisms (high-speed reciprocating motion mechanisms). This method is suitable for applications in industrial dispensing, die bonding machines, and semiconductor equipment where structural components require high-speed, micro-nano-level, high-precision reciprocating motion of more than 100 times per second. Background Technology

[0002] When designing displacement curves for high-speed reciprocating motion, a symmetrical S-shaped curve is typically used to ensure smooth, non-abrupt velocity at the beginning and end of the stroke. However, in practical applications, this curve cannot achieve rapid acceleration in the initial segment, thus limiting the motion frequency of the high-speed mechanism.

[0003] When designing displacement curves for high-speed reciprocating motion, ensuring continuous acceleration is generally a prerequisite for displacement curve design. However, in practical applications, this method struggles to eliminate sudden force changes in high-speed mechanisms. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a design method for an asymmetric S-shaped displacement curve suitable for high-speed mechanisms, which can achieve rapid acceleration in the initial segment of the curve and eliminate sudden changes in force in high-speed mechanisms.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] A method for designing asymmetric S-shaped displacement curves suitable for high-speed mechanisms includes:

[0007] Step 1: Divide the curve in high-speed reciprocating motion into time segments;

[0008] Step 2: Determine the order of the polynomials corresponding to each acceleration and deceleration curve based on the actual working conditions.

[0009] Step 3: Set the number of optimization attempts i = 1;

[0010] Step 4: Determine the acceleration values ​​for the constant acceleration segment;

[0011] Step 5: Construct acceleration curves for the acceleration and deceleration segments in high-speed reciprocating motion using monotonic higher-order polynomial curves with zero derivatives at both ends or even higher-order derivatives, so that at least one derivative at both ends of the acceleration and deceleration segments is zero.

[0012] Step 6: Construct the acceleration curve over the entire time domain, connecting the acceleration segment, constant acceleration segment, and deceleration segment end to end in the time domain to obtain the piecewise acceleration function;

[0013] Step 7: Determine whether the piecewise acceleration function is continuous. At the discontinuities, ensure that the magnitude of the acceleration in the constant acceleration segment remains unchanged. Adjust the coefficients to make the values ​​at both ends of the acceleration and deceleration segments equal to the values ​​at both ends of the constant acceleration segment.

[0014] Step 8: Integrate the piecewise acceleration function to obtain the piecewise velocity function for high-speed reciprocating motion. To ensure the continuity of the piecewise velocity function, values ​​need to be assigned to the lower-order coefficients and constant terms.

[0015] Step 9: Integrate the piecewise velocity function to obtain the piecewise displacement function of high-speed reciprocating motion. At the same time, in order to ensure the continuity of the piecewise displacement function, values ​​need to be assigned to the lower-order coefficients and constant terms.

[0016] Step 10: Determine whether the difference between the currently calculated maximum displacement and the designed maximum displacement is less than the maximum allowable displacement error. If not, change the acceleration value of the constant acceleration segment and proceed to step 4. If yes, proceed to the next step.

[0017] Step 11: Calculate the product of acceleration and velocity, and find the maximum absolute value of the product;

[0018] Step 12: Determine whether the number of optimization attempts is greater than or equal to the preset number of optimization attempts. If not, change the acceleration values ​​of the time segment and the constant acceleration segment, increment the number of optimization attempts i by 1, and go to step 4. If yes, proceed to the next step.

[0019] Step 13: Select the smallest absolute value among the maximum values ​​of the product of acceleration and velocity, obtain the acceleration values ​​of the corresponding time segment and constant acceleration segment, and the polynomial coefficients of each segment, and recalculate the piecewise acceleration function, velocity function, and displacement function using the new parameters;

[0020] Step 14: Dimensionless processing is performed on the piecewise displacement function.

[0021] Furthermore, step 6 includes:

[0022] A displacement stagnation point is set at the end of the displacement, that is, when the end of the mechanism reaches the maximum displacement value, the entire mechanism maintains its posture unchanged for a short period of time.

[0023] Furthermore, step 8 includes:

[0024] Step 81: Determine whether the initial and final velocities are 0. If not, solve for the boundary conditions of the peak value of the piecewise acceleration function and the settings of each time node.

[0025] Step 82: Change the acceleration values ​​for the time segment and the constant acceleration segment, and then proceed to Step 4.

[0026] Furthermore, step 9 includes:

[0027] Step 91: Determine if the initial displacement is 0 and if the displacement endpoint is S. max If not, then solve for the peak value of the piecewise acceleration function and the boundary conditions for each time node.

[0028] Step 92: Change the acceleration values ​​for the time segment and the constant acceleration segment, and then proceed to Step 4.

[0029] Furthermore, step 10 includes:

[0030] Step 101: If the current calculated maximum displacement is less than the designed target maximum displacement, and the difference between the two is greater than the maximum allowable displacement error, then increase the acceleration value of the constant acceleration segment and proceed to step 4.

[0031] Furthermore, step 10 includes:

[0032] Step 101': If the current calculated maximum displacement is greater than the designed target maximum displacement, and the difference between the two is greater than the maximum allowable displacement error, then reduce the acceleration value of the constant acceleration segment and proceed to step 4.

[0033] Furthermore, step 14 includes:

[0034] The displacement piecewise function is scaled according to the operating conditions.

[0035] The present invention has the following beneficial effects:

[0036] The present invention provides an asymmetric S-shaped displacement curve design method applicable to high-speed mechanisms, which improves upon commonly used acceleration curves, ensuring that higher-order derivative curves such as the jump curve remain smooth and continuous, thereby enhancing the continuity characteristic value of the displacement curve function and allowing for segmented adjustment of the acceleration degree.

[0037] This invention not only considers the higher-order differentiability of the curve but also optimizes the product of the mechanism's velocity and acceleration, controlling the dynamic force or torque at the input end and reducing the balancing torque or force. This not only improves the accuracy of the end-effector displacement but also stabilizes the mechanical environment of the mechanism, significantly reducing vibration throughout the entire motion and thus minimizing the impact of inertial loads on motion accuracy. The engineering implementation results are significant. This invention enables rapid acceleration at the beginning of the curve and eliminates abrupt force changes in high-speed mechanisms. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the asymmetric S-shaped displacement curve design method applicable to high-speed mechanisms according to the present invention.

[0039] Figure 2 This is an image of the monotonic intervals of the higher-order polynomial function in this invention;

[0040] Figure 3 This is the image of the piecewise acceleration function in this invention;

[0041] Figure 4 This is the image of the piecewise velocity function in this invention;

[0042] Figure 5 This is the image of the piecewise displacement function in this invention;

[0043] Figure 6 This is a piecewise function graph of the product of acceleration and velocity in this invention;

[0044] Figure 7 This is an example image of the curve spectrum of the mechanical optimization process in this invention. Detailed Implementation

[0045] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0046] To address the design deficiencies of existing high-speed reciprocating motion curves, this invention proposes an asymmetric S-shaped arbitrary displacement curve design method based on polynomial acceleration laws. This method improves upon commonly used acceleration curves, ensuring that higher-order derivative curves such as jump curves remain smooth and continuous, enhancing the continuity characteristics of the displacement curve function, and allowing for segmented adjustment of the acceleration degree.

[0047] This invention provides a method for designing asymmetric S-shaped displacement curves suitable for high-speed mechanisms, such as... Figure 1 As shown, it includes:

[0048] Step 1: Divide the curve in high-speed reciprocating motion into time segments;

[0049] In this step, time can be segmented based on experience, and the segment time node can be defined as t. i Where i = 0, 1, 2, ..., n, ..., m. t0 is the initial time, t n t is the process termination time. m This is the return trip end time. The number of segments can be flexibly set as needed, for example, 10-30 segments.

[0050] Step 2: Determine the order of the polynomials corresponding to each acceleration and deceleration curve based on the actual working conditions.

[0051] Step 3: Set the number of optimization attempts i = 1;

[0052] Step 4: Determine the acceleration values ​​for the constant acceleration segment;

[0053] Step 5: Construct acceleration curves for the acceleration and deceleration segments in high-speed reciprocating motion using monotonic higher-order polynomial curves with zero derivatives at both ends or even higher-order derivatives, so that at least one derivative at both ends of the acceleration and deceleration segments is zero.

[0054] In this step, the higher-order polynomial function used can be Figure 2 The solid line segment represents a curve. This segment is monotonically increasing or decreasing, and the derivatives, even higher-order derivatives, at both ends of the segment are zero. This higher-order polynomial can be of order 2, 3, or higher. The order of this higher-order polynomial can differ at different time points.

[0055] Step 6: Construct the acceleration curve over the entire time domain, connecting the acceleration segment, constant acceleration segment, and deceleration segment end to end in the time domain to obtain the piecewise acceleration function;

[0056] In this step, the piecewise acceleration function can be defined as a i (t), where i = 1, 2, ..., n, ..., m. A concrete example of a piecewise acceleration function can be seen as follows: Figure 3 , Figure 3 The curves shown are merely examples used to illustrate the methods and processes of curve construction.

[0057] This invention is designed based on acceleration, ensuring the continuity of acceleration rather than directly designing the displacement curve. The displacement curve is an arbitrary S-shaped displacement curve, which can be symmetrical or asymmetrical, thus facilitating the improvement of the initial velocity. The acceleration curve of the displacement curve is composed of curves corresponding to higher-order polynomials during the acceleration and deceleration phases. The continuity characteristic value of the displacement curve function can be improved by adjusting the order of the higher-order polynomials.

[0058] Assuming time segments are as follows Figure 3 As shown; the maximum forward acceleration is h1; the maximum reverse acceleration is h2; the stroke and return laws of the mechanism are symmetrical about time node t7.

[0059] To ensure end-efficiency, the mechanism is designed to remain stationary at the end point for a short period, maintaining zero acceleration and velocity while retaining its maximum displacement, as shown in the diagram between time points t6 and t8. In other words, a displacement stagnation point is set at the end of the displacement, meaning that when the end point reaches its maximum displacement, the entire mechanism maintains its position for a short time.

[0060] To simplify the description, this paper uses the cubic polynomial acceleration law as an example to illustrate the invention. It should be noted that this embodiment is merely for the convenience of explaining the design method involved in the invention and is only one example.

[0061] like Figure 2 As shown, for a cubic function with two stationary points A(x1, y1) and B(x2, y2), its general formula is:

[0062]

[0063] Construct the acceleration curve using the curve segment and straight line between points A and B, ensuring that the curve is tangent to the straight line segment.

[0064] The velocity function corresponding to the acceleration of the curve segment within the time interval is:

[0065]

[0066] The displacement function corresponding to the acceleration of the curve segment within the time interval is:

[0067]

[0068] The jump function of the acceleration of the curve segment within the corresponding time interval is:

[0069]

[0070] Where C1 and C2 are undetermined coefficients that ensure the continuity of the velocity function and the displacement function, respectively.

[0071] From the above, it is easy to see that its jump function is globally continuous in the time domain, which will not be explained further here.

[0072] During the process phase, its continuous piecewise acceleration function is:

[0073]

[0074] f2 = h1 x∈(t1,t2)

[0075]

[0076]

[0077] f5 = h2 x∈(t4,t5)

[0078]

[0079] f7 = 0 x∈(t6,t7)

[0080] Step 7: Determine whether the piecewise acceleration function is continuous. At the discontinuities, ensure that the magnitude of the acceleration in the constant acceleration segment remains unchanged. Adjust the coefficients to make the values ​​at both ends of the acceleration and deceleration segments equal to the values ​​at both ends of the constant acceleration segment.

[0081] Step 8: Integrate the piecewise acceleration function to obtain the piecewise velocity function for high-speed reciprocating motion. To ensure the continuity of the piecewise velocity function, values ​​need to be assigned to the lower-order coefficients and constant terms.

[0082] In this step, the piecewise velocity function can be defined as V. i (t), where i = 1, 2, ..., n, ..., m. A concrete example of a piecewise velocity function can be seen as follows: Figure 4 .

[0083] As an optional embodiment, step 8 includes:

[0084] Step 81: Determine whether the initial and final velocities are 0. If not, solve for the boundary conditions of the peak value of the piecewise acceleration function and the settings of each time node.

[0085] In this step, we determine whether V0 = 0, Vn = 0, and Vm = 0. If not, then we apply the boundary condition that the velocities at both ends of the displacement are 0 (i.e., V1(0) = 0). and Please provide a solution.

[0086] Step 82: Change the acceleration values ​​for the time segment and the constant acceleration segment, and then proceed to Step 4.

[0087] In the specific example above, during the process phase, its continuous piecewise velocity function is:

[0088]

[0089] v2 = h1x + Cv2 x∈(t1,t2)

[0090]

[0091]

[0092] v5 = h2x + Cv5 x∈(t4,t5)

[0093]

[0094] v7 = 0 x ∈ (t6, t7)

[0095] Among them, Cv2, Cv3, Cv4, Cv5, and Cv6 are undetermined coefficients that ensure the continuity of the velocity function, and can be solved based on the continuity.

[0096] Step 9: Integrate the piecewise velocity function to obtain the piecewise displacement function of high-speed reciprocating motion. At the same time, in order to ensure the continuity of the piecewise displacement function, values ​​need to be assigned to the lower-order coefficients and constant terms.

[0097] In this step, the piecewise displacement function can be defined as S. i (t), where i = 1, 2, ..., n, ..., m. A concrete example of a piecewise displacement function can be seen as follows: Figure 5 .

[0098] As an optional embodiment, step 9 includes:

[0099] Step 91: Determine if the initial displacement is 0 and if the displacement endpoint is S. max If not, then solve for the peak value of the piecewise acceleration function and the boundary conditions for each time node.

[0100] In this step, we determine whether S0 = 0 and Sn = S. max And Sm = 0; otherwise, then based on the boundary condition of displacement (i.e., S1(0) = 0), and Please provide a solution.

[0101] Step 92: Change the acceleration values ​​for the time segment and the constant acceleration segment, and then proceed to Step 4.

[0102] In the specific example above, during the process phase, its continuous piecewise displacement function is:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] Among them, Cs2, Cs4, Cs5, and Cs6 are undetermined coefficients that ensure the continuity of the displacement function, and can be solved based on the continuity.

[0111] To ensure the stroke ends at x = t n and the return journey endpoint x = t m When the speed is zero, it is necessary to:

[0112] and

[0113] The boundary conditions for velocity are:

[0114]

[0115] Due to symmetry, the current parameter always satisfies:

[0116] S1(0) = 0, and

[0117] At this point, the nodes of the time segment and the peak values ​​of each acceleration segment have been determined. The graphs of acceleration, velocity, displacement, and the product of acceleration and velocity are shown below. Figure 3 , Figure 4 , Figure 5 and Figure 6 .

[0118] Step 10: Determine whether the difference between the currently calculated maximum displacement and the designed maximum displacement is less than the maximum allowable displacement error based on the displacement piecewise function. If not, change the acceleration value of the constant acceleration segment and proceed to step 4. If yes, proceed to the next step.

[0119] This step involves determining whether the maximum displacement meets the design requirements. If the displacement is too large, h1 is decreased; if the displacement is too small, h1 is increased. This process is repeated to control the displacement. This invention targets the maximum displacement, ensuring the design accuracy of the displacement.

[0120] Figure 1 In this context, S represents the current calculated maximum displacement, S0 represents the designed target maximum displacement, and ΔS represents the maximum allowable displacement error.

[0121] As an optional embodiment, step 10 includes:

[0122] Step 101: If the current calculated maximum displacement is less than the designed target maximum displacement, and the difference between the two is greater than the maximum allowable displacement error (i.e., S0-S>△S), then increase the acceleration value of the constant acceleration segment and proceed to step 4.

[0123] As another optional embodiment, step 10 includes:

[0124] Step 101': If the current calculated maximum displacement is greater than the designed target maximum displacement, and the difference between the two is greater than the maximum allowable displacement error (i.e., S-S0 > ΔS), then reduce the acceleration value of the constant acceleration segment and proceed to step 4.

[0125] It is understandable that if the current calculated maximum displacement S is equal to the designed target maximum displacement S0, then the difference between the two is within the allowable maximum displacement error, and the next step can be executed.

[0126] Step 11: Calculate the product of acceleration and velocity, and find the maximum absolute value of the product;

[0127] In this step, the product of acceleration and velocity is calculated, i.e., the function M(t) = V. i (t)a i Find the function M(t) and solve for the maximum absolute value. A concrete example of the function M(t) can be found as follows: Figure 6 .

[0128] Step 12: Determine whether the number of optimization attempts is greater than or equal to the preset number of optimization attempts. If not, change the acceleration values ​​of the time segment and the constant acceleration segment, increment the number of optimization attempts i by 1, and go to step 4. If yes, proceed to the next step.

[0129] This step is the mechanical optimization. In this step, the time segment nodes and h1 can be changed to optimize various parameters while ensuring the displacement requirements are met. The optimization criterion is |M max |Minimum. The curve spectra of each curve in the optimization process are as follows: Figure 7 In the design of the S-shaped displacement curve, the time segment nodes involved in this invention can be adjusted arbitrarily within a certain range, and the acceleration law and peak value of each segment can also be adjusted arbitrarily within a certain range. This adjustment is subject to constraints, which are based on the premise that the maximum displacement remains unchanged or remains within a certain range.

[0130] This invention achieves a minimum peak value for the function M(t) and a smoother performance by iteratively calculating changes to the peak acceleration value and the time segmentation node settings. Figure 1 In this context, j represents the number of optimization attempts, and its specific value can be flexibly set as needed, such as 50, 100, 200, etc.

[0131] Step 13: Select the smallest absolute value among the maximum values ​​of the product of acceleration and velocity, obtain the acceleration values ​​of the corresponding time segment and constant acceleration segment, and the polynomial coefficients of each segment, and recalculate the piecewise acceleration function, velocity function, and displacement function using the new parameters;

[0132] In this step, |M is extracted. max The displacement curve is recalculated by minimizing the corresponding parameters. This invention uses minimizing the product of acceleration and velocity as a constraint, with the ultimate goal of ensuring displacement stroke. The optimization of the curve is based on minimizing the peak value of the product of acceleration and velocity, thereby reducing the impact of inertial load on motion accuracy. In this way, not only are the dynamic effects of acceleration and jump on the mechanism's motion considered, but also the dynamic effects of the variation law of the product of velocity and acceleration on the mechanism's motion.

[0133] Step 14: Dimensionless processing is performed on the piecewise displacement function.

[0134] In this step, the displacement piecewise curve is dimensionlessly processed and stored as a general curve for similar mechanisms. Specifically, the displacement piecewise function can be scaled according to the working conditions to accommodate displacement paths of different lengths. Dimensionlessness processing is a standard technique in this field and will not be elaborated upon here.

[0135] For high-speed mechanisms, the equilibrium torque corresponding to the inertial load is the dynamic torque M. d Its expression is approximately: M d =Km / ω·V·a (where K is a coefficient, m is the equivalent mass of the mechanism, ω is the input rotational speed, V is the equivalent velocity of the mechanism, and a is the equivalent acceleration of the mechanism. In mechanisms where the transmission ratio does not change significantly, M can be approximated as...) d ∝m / ω·V·a). The balancing force of the inertial load also has the same form. In order to reduce the balancing torque or balancing force at the input, this invention considers the optimization of the product of the mechanism's velocity and acceleration and its peak value.

[0136] In summary, the asymmetric S-shaped displacement curve design method of the present invention, applicable to high-speed mechanisms, improves upon commonly used acceleration curves, ensuring that higher-order derivative curves such as the jump curve remain smooth and continuous, thereby enhancing the continuity characteristic value of the displacement curve function and allowing for segmented adjustment of the acceleration degree.

[0137] This invention not only considers the higher-order differentiability of the curve, but also optimizes the product of the mechanism's velocity and acceleration, as well as its peak value. It controls the dynamic force or torque at the input end, reducing the balancing torque or force at the input. This not only improves the accuracy of the end-effector displacement but also stabilizes the mechanical environment of the mechanism, significantly reducing vibration throughout the entire motion. This reduces the impact of inertial loads on motion accuracy, resulting in significant engineering implementation benefits.

[0138] This invention performs dimensionless processing on the displacement curve, making it usable as a universal curve for similar mechanisms. Simultaneously, it can also meet the needs of different displacements at different periods for the same mechanism (i.e., different periods have different amplification factors for the global displacement).

[0139] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for designing asymmetric S-shaped displacement curves suitable for high-speed mechanisms, characterized in that, include: Step 1: Divide the curve in high-speed reciprocating motion into time segments; Step 2: Determine the order of the polynomials corresponding to each acceleration and deceleration curve based on the actual working conditions. Step 3: Set the number of optimization attempts i=1; Step 4: Determine the acceleration values ​​for the constant acceleration segment; Step 5: Construct acceleration curves for the acceleration and deceleration segments in high-speed reciprocating motion using monotonic higher-order polynomial curves with zero first or higher-order derivatives at both ends, so that at least one first-order derivative at both ends of the acceleration and deceleration segments is zero. Step 6: Construct the acceleration curve over the entire time domain, connecting the acceleration segment, constant acceleration segment, and deceleration segment end to end in the time domain to obtain the piecewise acceleration function; Step 7: Determine whether the piecewise acceleration function is continuous. At the discontinuities, ensure that the magnitude of the acceleration in the constant acceleration segment remains unchanged. Adjust the coefficients to make the values ​​at both ends of the acceleration and deceleration segments equal to the values ​​at both ends of the constant acceleration segment. Step 8: Integrate the piecewise acceleration function to obtain the piecewise velocity function for high-speed reciprocating motion. To ensure the continuity of the piecewise velocity function, values ​​need to be assigned to the lower-order coefficients and constant terms. Step 9: Integrate the piecewise velocity function to obtain the piecewise displacement function of high-speed reciprocating motion. At the same time, in order to ensure the continuity of the piecewise displacement function, values ​​need to be assigned to the lower-order coefficients and constant terms. Step 10: Determine whether the difference between the currently calculated maximum displacement and the designed maximum displacement is less than the maximum allowable displacement error. If not, change the acceleration value of the constant acceleration segment and proceed to step 4. If yes, proceed to the next step. Step 11: Calculate the product of acceleration and velocity, and find the maximum absolute value of the product; Step 12: Determine whether the number of optimization attempts is greater than or equal to the preset number of optimization attempts. If not, change the acceleration values ​​of the time segment and the constant acceleration segment, increment the number of optimization attempts i by 1, and go to step 4. If yes, proceed to the next step. Step 13: Select the smallest absolute value among the maximum values ​​of the product of acceleration and velocity, obtain the acceleration values ​​of the corresponding time segment and constant acceleration segment, and the polynomial coefficients of each segment, and recalculate the piecewise acceleration function, velocity function, and displacement function using the new parameters; Step 14: Dimensionless processing is performed on the piecewise displacement function; In step 6, for a cubic function with two stationary point coordinates A(x1, y1) and B(x2, y2), its general formula is: ； Construct the acceleration curve using the curve segment and straight line segment between points A and B, ensuring that the curve segment is tangent to the straight line segment; The velocity function corresponding to the acceleration of the curve segment within the time interval is: ； The displacement function corresponding to the acceleration of the curve segment within the time interval is: ； The jump function of the acceleration of the curve segment within the corresponding time interval is: ； Where C1 and C2 are undetermined coefficients that ensure the continuity of the velocity function and the displacement function, respectively.

2. The method according to claim 1, characterized in that, Step 6 includes: A displacement stagnation point is set at the end of the displacement, that is, when the end of the mechanism reaches the maximum displacement value, the entire mechanism maintains its posture unchanged for a short period of time.

3. The method according to claim 1, characterized in that, Step 8 includes: Step 81: Determine whether the initial and final velocities are 0. If not, solve for the boundary conditions of the peak value of the piecewise acceleration function and the settings of each time node. Step 82: Change the acceleration values ​​for the time segment and the constant acceleration segment, and then proceed to Step 4.

4. The method according to claim 1, characterized in that, Step 9 includes: Step 91: Determine if the initial displacement is 0 and if the displacement endpoint is... If not, then solve for the peak value of the piecewise acceleration function and the boundary conditions for each time node; the boundary conditions are: , ,and The piecewise displacement function is defined as follows: ,i=1,2,…,n,…,m, For acceleration; Step 92: Change the acceleration values ​​for the time segment and the constant acceleration segment, and then proceed to Step 4.

5. The method according to claim 1, characterized in that, Step 10 includes: Step 101: If the current calculated maximum displacement is less than the designed target maximum displacement, and the difference between the two is greater than the maximum allowable displacement error, then increase the acceleration value of the constant acceleration segment and proceed to step 4.

6. The method according to claim 1, characterized in that, Step 10 includes: Step 101': If the current calculated maximum displacement is greater than the designed target maximum displacement, and the difference between the two is greater than the maximum allowable displacement error, then reduce the acceleration value of the constant acceleration segment and proceed to step 4.

7. The method according to claim 1, characterized in that, Step 14 includes: The displacement piecewise function is scaled according to the operating conditions.

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