A hybrid electronic cam curve generation method with controllable curvature based on Hermite interpolation

Abstract

The present invention discloses a method for generating a hybrid electronic cam curve with controllable curvature based on Hermite interpolation, comprising the following steps: S1: real-time interpolation parameter offline preprocessing: according to the input driving shaft driven shaft pairing point sequence, a differential calculation method is used to obtain the first-order, second-order and third-order mixed difference quotients at each pairing point as the endpoint derivative value of Hermite interpolation; then according to the curve fitting coefficient, the endpoint derivative value at each pairing point is corrected to adjust the curvature of the Hermite interpolation curve; then according to the straight line-curve mixing coefficient, the endpoint derivative value at each pairing point is corrected again to ensure the high-order continuity at the connection between the straight line segment and the curve segment. The present invention generates a straight line segment-curve segment mixed high-order smooth cam curve with controllable curvature of the curve segment according to the input driving shaft driven shaft point sequence, as well as the curve deviation coefficient and the straight line-curve mixing coefficient required by the customer.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic cam control, and specifically to a method for generating a hybrid electronic cam curve with controllable bending degree based on Hermite interpolation. Background Art

[0002] The electronic cam synchronization function is a series of PLopen standard instructions and is widely used in production practices such as tool turning and fly cutting. Cam synchronization mainly realizes the movement of the driven shaft following the driving shaft. It mainly requires that in key points and key line segments, the movement position relationship between the driving shaft and the driven shaft meets the requirements. Therefore, according to the application scenarios of cam synchronization, the format of the cam synchronization input instruction is a series of point data, line segments, and combinations of line segments and points. However, when using high-order curves to achieve the transition of the electronic cam curve, problems such as excessive bending degree of the transition curve trajectory are likely to occur, and in most electronic cam functions, the bending degree of the cam curve cannot be adjusted. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for generating a hybrid electronic cam curve with controllable bending degree based on Hermite interpolation to solve the problems in the prior art.

[0004] To achieve the above purpose, the present invention provides the following technical solution: A method for generating a hybrid electronic cam curve with controllable bending degree based on Hermite interpolation, including the following steps:

[0005] S1: Offline preprocessing of real-time interpolation parameters: According to the input paired point sequence of the driving shaft and the driven shaft, the first-order, second-order, and third-order mixed difference quotients at each paired point are obtained by using the difference calculation method as the endpoint derivative values of Hermite interpolation; then, according to the curve fitting coefficient, the endpoint derivative values at each paired point are corrected to adjust the bending degree of the Hermite interpolation curve; then, according to the straight-line - curve mixing coefficient, the endpoint derivative values at each paired point are corrected again to ensure the high-order continuity at the connection of the straight-line segment and the curve segment; finally, according to the input paired point sequence of the driving shaft and the driven shaft and the generated endpoint derivative values, a cubic, quintic, or septic Hermite interpolation function is constructed according to customer requirements to perform the transition between each point of the curve segment.

[0006] S2: Hermite real-time interpolation operation: During the real-time interpolation operation, first, find the paired point sequence segment where the real-time position of the driving shaft is located according to the input real-time position of the driving shaft; then, according to the straight-line - curve mixing coefficient, determine whether the driving shaft position uses a straight-line transition or a curve transition; if it is a straight-line transition, the position of the driven shaft will be obtained by using a straight-line interpolation form; if it is a curve transition, the position of the driven shaft is calculated according to the constructed Hermite interpolation curve.

[0007] Preferably, the S1 specifically includes the following steps:

[0008] S1.1: Hermite interpolation endpoint derivative value: According to the input driving shaft driven shaft pairing point sequence, the differential calculation method is used to obtain the first-order, second-order and third-order mixed difference quotients at each pairing point as the endpoint derivative value of Hermite interpolation; for the driving shaft position point sequence M:[x 0 ,…,x i ,…,x n ], the driven axis has a corresponding position point sequence S: [y 0 ,…,y i ,…,y n ] corresponds to the first-order derivative of the driven shaft at each position point relative to Obtained through mixed difference quotient;

[0009]

[0010] Where i=0,1,2…,n-1; when i=n,

[0011] Second-order derivative And the third-order derivative It is also obtained through the mixed difference quotient method, and the calculation formulas are:

[0012]

[0013] Where i=0,1,2…,n-1; when i=n,

[0014]

[0015] Where i=0,1,2…,n-1; when i=n,

[0016] S1.2: According to the curve fitting coefficient α at each segment: [α 0 ,…,α i ,…,α n ] Correction derivative value: According to the curve fitting coefficient, when a certain segment B(x i+1 ,y i+1 )} at the curve fitting coefficient α i When is larger, the curve deviates less from the straight line segment and the curvature is lower; since the interpolation curve is mainly based on this segment The derivative value at the endpoint is determined, so the segment needs to be corrected according to the curve fitting coefficient The derivative value at the endpoint; through the fitting coefficient, increase the segment The proportion of the first-order derivative value of the slope of the straight line at the two end points is calculated as follows:

[0017]

[0018] The second - order and third - order derivative values at each point need to be recalculated according to the corrected first - order derivative values;

[0019] S1.3: Correction of derivative values at the endpoints of the straight - line segment: In the hybrid cam curve, according to customer requirements, a straight - line segment is used for transition between two points A(x i , y i ), B(x i+1 , y i+1 ); To ensure the high - order continuity of this segment with other curve segments, it is necessary to correct the high - order derivative values at the two endpoints of this straight - line segment; According to the properties of a straight line, the first - order derivative of a straight - line segment is its slope, and the second - order and higher - order derivatives are zero; Then the derivative corrections at the two endpoints A and B of the specified straight - line segment are: transition; To ensure the high - order continuity of this segment with other curve segments, it is necessary to correct the high - order derivative values at the two endpoints of this straight - line segment; According to the properties of a straight line, the first - order derivative of a straight - line segment is its slope, and the second - order and higher - order derivatives are zero; Then the derivative corrections at the two endpoints A and B of the specified straight - line segment are: at both endpoints A and B of the straight - line segment are corrected as:

[0020]

[0021]

[0022]

[0023] S1.3: Generation of Hermite interpolation coefficients for the curve segment: According to the sequence points given by the customer, for the driving shaft: M:[x 0 ,…,x i ,…,x n , and the driven shaft S:[y 0 ,…,y i ,…,y n , as well as the calculated first - order derivative values second - order derivative values and third - order derivative values calculate the Hermite interpolation coefficients for the transition part of the curve; Use cubic, quintic, and septic Hermite polynomials to perform transitions between the given position sequences of the driving and driven shafts; For two points A(x i , y i ), B(x i+1 , y i+1 ), the calculation formula for the transition using the Hermite interpolation polynomial is:

[0024] (4) Cubic Hermite interpolation algorithm: In the transition region, use the cubic Hermite interpolation algorithm to achieve the transition and ensure second - order continuity at the connection points; The transition curve mainly constructs a cubic polynomial curve based on the first - order derivatives at the starting and ending points to achieve the transition; The cubic polynomial curve is obtained through Hermite interpolation. The expression of the interpolation polynomial is:

[0025]

[0026] In the formula, x is the real-time position value of the driving shaft; let h = x i+1 -x i , then

[0027]

[0028]

[0029]

[0030]

[0031] (5) Quintic Hermite interpolation algorithm: In the transition region, the quintic Hermite interpolation algorithm is used to achieve the transition, ensuring third-order continuity at the connection points. The transition curve is mainly constructed based on the first and second derivatives at the starting and ending points to form a quintic polynomial curve for the transition; the quintic polynomial curve is obtained through Hermite interpolation; the expression of the interpolation polynomial is:

[0032]

[0033] In the formula, x is the real-time position value of the driving shaft; let h = x i+1 -x i , then

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] (6) Septic Hermite interpolation algorithm: In the transition region, the septic Hermite interpolation algorithm is used to achieve the transition, ensuring fourth-order continuity at the connection points; the transition curve is mainly constructed based on the first, second, and third derivatives at the starting and ending points to form a septic polynomial curve for the transition; the septic polynomial curve is obtained through Hermite interpolation; the expression of the interpolation polynomial is:

[0041]

[0042] In the formula, x is the real-time position value of the driving shaft. Let h = x i+1 -x i , then

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] Preferably, in the step S2: Hermite real-time interpolation operation: perform real-time interpolation operation according to the curve equation parameters generated by preprocessing; the main function of the real-time interpolation operation is to calculate the corresponding driven shaft position value in real time according to the input active shaft position value; first, determine the number of segments of the hybrid cam curve where the received active shaft position x is located, and select the real-time interpolation function according to whether the segment transitions according to a straight line or a curve segment; let the current real-time position of the active shaft be x, and the number of segments of the hybrid cam curve where it is located be the i-th segment.

[0052] (2) When the i-th segment is a straight line transition, let the position of the driven shaft be y, and the real-time interpolation program is:

[0053]

[0054] (2) When the i-th segment uses a curve transition; according to the requirements of cam high-order fairness, select to use the methods of formulas (6), (8), or (10) to achieve cubic, quintic, or septic curve transitions; let the position of the driven shaft be y, and the real-time interpolation programs are respectively:

[0055] When the selected cam curve is cubic:

[0056]

[0057] When the selected cam curve is quintic:

[0058]

[0059] When the selected cam curve is septic:

[0060]

[0061] Compared with the prior art, the beneficial effects of the present invention are as follows: Hermite interpolation of three times, five times, and seven times is adopted to realize the interpolation of the motion position relationship between the driving shaft and the driven shaft. Correspondingly, it can ensure that the driving shaft and the driven shaft achieve second-order continuity (velocity continuity), third-order continuity (acceleration continuity), and fourth-order continuity (jerk continuity); the driven shaft of the present invention supports multiple shafts; by introducing the curve fitting coefficient and the endpoint derivative value correction, the present invention solves the problems that in the generation of the existing cam curve, the bending degree of the curve is uncontrollable, and in the generation of the hybrid cam curve, it is easy to generate a high-order non-smooth transition between the straight line segment and the curve segment. Description of the Drawings

[0062] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0063] Figure 1 Experimental 1 Cubic Hermite interpolation cam curve;

[0064] Figure 2 Experimental 1 Quintic Hermite interpolation cam curve;

[0065] Figure 3 Experimental 1 Septic Hermite interpolation cam curve;

[0066] Figure 4 Experimental 2 Cubic Hermite interpolation cam curve;

[0067] Figure 5 Experimental 2 Quintic Hermite interpolation cam curve;

[0068] Figure 6 Experimental 2 Septic Hermite interpolation cam curve;

[0069] Figure 7 Experimental 3 Cubic Hermite interpolation cam curve;

[0070] Figure 8 Experimental 3 Quintic Hermite interpolation cam curve;

[0071] Figure 9 Experimental 3 Septic Hermite interpolation cam curve;

[0072] Figure 10 Experimental 4 Cubic Hermite interpolation cam curve;

[0073] Figure 11 Experimental 4 Quintic Hermite interpolation cam curve;

[0074] Figure 12 Experimental 4 Septic Hermite interpolation cam curve;

[0075] Figure 13Experiment 5 Cubic Hermite Interpolation Cam Curve;

[0076] Figure 14 Experiment 5 Quintic Hermite Interpolation Cam Curve;

[0077] Figure 15 Experiment 5 Septic Hermite Interpolation Cam Curve;

[0078] Figure 16 Experiment 6 Cubic Hermite Interpolation Cam Curve;

[0079] Figure 17 Experiment 6 Quintic Hermite Interpolation Cam Curve;

[0080] Figure 18 Experiment 6 Septic Hermite Interpolation Cam Curve;

[0081] Figure 19 Flowchart of the present invention. Detailed implementation manners

[0082] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0083] As Figure 19 , in an embodiment of the present invention, a method for generating a hybrid electronic cam curve with controllable bending degree based on Hermite interpolation includes the following steps:

[0084] S1: Offline preprocessing of real-time interpolation parameters: According to the input sequence of paired points of the active axis and the driven axis, the first-order, second-order, and third-order mixed difference quotients at each paired point are obtained by using the difference calculation method as the end derivative values of Hermite interpolation; then, according to the curve fitting coefficient, the end derivative values at each paired point are corrected to adjust the bending degree of the Hermite interpolation curve; then, according to the straight-line-curve mixing coefficient, the end derivative values at each paired point are corrected again to ensure the high-order continuity at the connection of the straight-line segment and the curve segment; finally, according to the input sequence of paired points of the active axis and the driven axis and the generated end derivative values, a cubic, quintic, or septic Hermite interpolation function is constructed according to customer requirements to perform transitions between points on the curve segment.

[0085] S2: Hermite real-time interpolation operation: During the real-time interpolation operation, first, find the sequence segment of paired points of the active axis and the driven axis where the real-time position of the active axis is located according to the input real-time position of the active axis; then, according to the straight-line-curve mixing coefficient, judge whether the straight-line transition or the curve transition is adopted for the position of the active axis; if it is a straight-line transition, the position of the driven axis will be obtained by using the straight-line interpolation form; if it is a curve transition, the position of the driven axis is calculated according to the constructed Hermite interpolation curve.

[0086] Preferably, the S1 specifically includes the following steps:

[0087] S1.1: End derivative values of Hermite interpolation: According to the input sequence of paired points of the active axis and the driven axis, the first-order, second-order, and third-order mixed difference quotients at each paired point are obtained by using the difference calculation method as the end derivative values of Hermite interpolation; for the active axis position point sequence M: [x 0 , …, x i , …, x n , there is a corresponding position point sequence S: [y 0 , …, y i , …, y n of the driven axis corresponding to it; the first-order derivative of the driven axis relative to each position point

[0088] is obtained in the form of mixed difference quotient. is obtained in the form of mixed difference quotient.

[0089]

[0090] where i = 0, 1, 2 …, n - 1; when i = n,

[0091] the second-order derivative and the third-order derivative are also obtained by the mixed difference quotient method, and the calculation formulas are respectively:

[0092]

[0093] where \(i = 0, 1, 2, \cdots, n - 1\); when \(i = n\),

[0094]

[0095] where \(i = 0, 1, 2, \cdots, n - 1\); when \(i = n\),

[0096] S1.2: According to the curve fitting coefficient \(\alpha\) at each segment: \([\alpha 0 , \cdots, \alpha i , \cdots, \alpha n \) to correct the derivative value: According to the curve fitting coefficient, when the curve fitting coefficient \(\alpha B(x i+1 , y i+1 )\) at a certain point is larger, the degree of deviation of the curve from the straight line segment at this segment is lower, and the degree of bending is lower; since the interpolation curve is mainly determined based on the derivative values at the endpoints of this segment, it is necessary to correct the derivative values at the endpoints of this segment according to the curve fitting coefficient; through the fitting coefficient, increase the proportion of the first-order derivative values of the straight line slope at the two endpoints at this segment, and the calculation formula is as follows: i The second-order and third-order derivative values at each point need to be recalculated according to the corrected first-order derivative values; The derivative values at the endpoints of this segment need to be corrected; The derivative values at the endpoints of this segment; The proportion of the first-order derivative value of the straight line slope at the two endpoints at this segment, and the calculation formula is as follows:

[0097]

[0098]

[0099]

[0100] The second-order and third-order derivative values at each point need to be recalculated according to the corrected first-order derivative values;

[0101] S1.3: Correction of derivative values at the endpoints of the straight line segment: In the hybrid cam curve, according to customer requirements, a straight line segment i , y i ), B(x i+1 , y i+1 ) is used for transition between two points A(x ; In order to ensure the high-order continuity of this segment with other curve segments, it is necessary to correct the high-order derivative values at the two endpoints of this straight line segment; According to the properties of the straight line, the first-order derivative of the straight line segment is its slope, and the second-order and higher-order derivatives are zero; then the derivative corrections at the two endpoints A and B of the specified straight line segment are as follows:

[0102]

[0103]

[0104]

[0105] S1.3: Hermite Interpolation Coefficient Generation for Curve Segments: Based on the sequence of points given by the customer, the active axis: M: [x 0 , …, x i , …, x n , the driven axis S: [y 0 , …, y i , …, y n , and the first derivative values, second derivative values and third derivative values at each point calculated, calculate the Hermite interpolation coefficients for the curve transition part; use cubic, quintic, and septic Hermite polynomials to perform transitions between the given position sequences of the active and driven axes; for two points A(x i , y i ), B(x i+1 , y i+1 ), the calculation formula for the transition using the Hermite interpolation polynomial is:

[0106] (7) Cubic Hermite Interpolation Algorithm: In the transition region, use the cubic Hermite interpolation algorithm to achieve the transition, ensuring second-order continuity at the connection points; the transition curve is mainly constructed based on the first derivatives at the starting and ending points to form a cubic polynomial curve for the transition; the cubic polynomial curve is obtained through Hermite interpolation. The expression of the interpolation polynomial is:

[0107]

[0108] In the formula, x is the real-time position value of the active axis; let h = x i+1 - x i , then

[0109]

[0110]

[0111]

[0112]

[0113] (8) Quintic Hermite Interpolation Algorithm: In the transition region, use the quintic Hermite interpolation algorithm to achieve the transition, ensuring third-order continuity at the connection points. The transition curve is mainly constructed based on the first and second derivatives at the starting and ending points to form a quintic polynomial curve for the transition; the quintic polynomial curve is obtained through Hermite interpolation; the expression of the interpolation polynomial is:

[0114]

[0115] Wherein, x is the real-time position value of the driving shaft; let h = x i+1 -x i , then

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] (9) Seventh-degree Hermite interpolation algorithm: In the transition region, the seventh-degree Hermite interpolation algorithm is used to achieve the transition, ensuring fourth-order continuity at the connection points; the transition curve is mainly constructed according to the first, second, and third derivatives at the starting point and the ending point to obtain a seventh-degree polynomial curve for the transition; the seventh-degree polynomial curve is obtained through Hermite interpolation; the expression of the interpolation polynomial is:

[0123]

[0124] Wherein, x is the real-time position value of the driving shaft. Let h = x i+1 -x i , then

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Preferably, in S2: Hermite real-time interpolation operation: According to the curve equation parameters generated by preprocessing, perform real-time interpolation operation; the main function of real-time interpolation operation is to calculate the corresponding driven shaft position value in real time according to the input active shaft position value; first, determine the number of segments of the hybrid cam curve where the received active shaft position x is located, and select the real-time interpolation function according to whether the segment transitions according to a straight line or a curve segment; let the current real-time position of the active shaft be x, and the number of segments of the hybrid cam curve it is in be the i-th segment

[0134] (3) When the i-th segment is a straight-line transition, let the position of the driven shaft be y, and the real-time interpolation program is:

[0135]

[0136] (2) When the i-th segment is a curve transition; according to the requirements of cam high-order fairness, select to use the methods of equations (6), (8), or (10) to achieve cubic, quintic, or septic curve transitions; let the position of the driven shaft be y, and the real-time interpolation programs are respectively:

[0137] When the selected cam curve is cubic:

[0138]

[0139] When the selected cam curve is quintic:

[0140]

[0141] When the selected cam curve is septic:

[0142]

[0143] Experimental verification

[0144] In order to verify the method proposed in this paper, different input parameters are used to verify the cam curve generation algorithm proposed in the present invention.

[0145] Experimental 1 initial data:

[0146] Active shaft: x = [1, 3, 4, 6, 9, 13, 15, 17, 18, 23, 25];

[0147] Driven shaft: y = [2, 5, 8, 10, 8, 6, 4, 3, 6, 9, 12];

[0148] Line segment and point identifier (when L is 1, it means this segment runs in a straight line): L = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

[0149] Curve fitting coefficient: α = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

[0150] Number of points: n = 11

[0151] Convex contour curve: as Figures 1-3 。

[0152] Initial data for Experiment 2:

[0153] Driving shaft: x = [1, 3, 4, 6, 9, 13, 15, 17, 18, 23, 25];

[0154] Driven shaft: y = [2, 5, 8, 10, 8, 6, 4, 3, 6, 9, 12];

[0155] Line segment and point identifier (when L is 1, it means this segment runs in a straight line): L = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0];

[0156] Curve fitting coefficient: α = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

[0157] Number of points: n = 11

[0158] Convex contour curve: as Figures 4-6 。

[0159] Initial data for Experiment 3:

[0160] Driving shaft: x = [1, 3, 4, 6, 9, 13, 15, 17, 18, 23, 25];

[0161] Driven shaft: y = [2, 5, 8, 10, 8, 6, 4, 3, 6, 9, 12];

[0162] Line segment and point identifier (when L is 1, it means this segment runs in a straight line): L = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

[0163] Curve fitting coefficient: α = [0, 0, 0, 0, 0, 0, 2, 0, 6, 0];

[0164] Number of points: n = 11

[0165] Convex contour curve: as Figures 7-9 。

[0166] Initial data for Experiment 4:

[0167] Driving shaft: x = [1, 3, 4, 6, 9, 13, 15, 17, 18, 23, 25, 27, 31];

[0168] Driven shaft: y = [2, 5, 8, 10, 28, 46, 34, 23, 16, 19, 12, 20, 27];

[0169] Line segment and point identifier (when L = 1, it means this segment runs in a straight line): L = [0,0,0,0,0,0,0,0,0,0,0,0];

[0170] Curve fitting coefficient: α = [0,0,0,0,0,0,0,0,0,0,0,0];

[0171] Number of points: n = 13

[0172] Convex contour curve: such as Figures 10-12 。

[0173] Initial data for Experiment 5:

[0174] Driving shaft: x = [1,3,4,6,9,13,15,17,18,23,25,27,31];

[0175] Driven shaft: y = [2,5,8,10,28,46,34,23,16,19,12,20,27];

[0176] Line segment and point identifier (when L = 1, it means this segment runs in a straight line): L = [0,0,0,0,1,0,0,0,1,0,0,0];

[0177] Curve fitting coefficient: α = [0,0,0,0,0,0,0,0,0,0,0,0];

[0178] Number of points: n = 13

[0179] Convex contour curve: such as Figures 13-15 。

[0180] Initial data for Experiment 6:

[0181] Driving shaft: x = [1,3,4,6,9,13,15,17,18,23,25,27,31];

[0182] Driven shaft: y = [2,5,8,10,28,46,34,23,16,19,12,20,27];

[0183] Line segment and point identifier (when L = 1, it means this segment runs in a straight line): L = [0,0,0,0,0,0,0,0,0,0,0,0];

[0184] Curve fitting coefficient: α = [0,0,0.5,0,1,0,0,0,3,0,0,0];

[0185] Number of points: n = 13

[0186] Convex contour curve: such as Figures 16-18 。

[0187] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A hybrid electronic cam curve generation method with controllable curvature based on Hermite interpolation, characterized by: The following steps are involved: S1: Offline preprocessing of real-time interpolation parameters: Based on the input sequence of paired points of the active shaft and the driven shaft, the differential calculation method is used to obtain the first-order, second-order and third-order mixed difference quotients at each paired point as the endpoint derivative values ​​of the Hermite interpolation; then, according to the curve fitting coefficient, the endpoint derivative values ​​at each paired point are corrected to adjust the curvature of the Hermite interpolation curve; then, according to the line-curve mixing coefficient, the endpoint derivative values ​​at each paired point are further corrected to ensure the high-order continuity at the connection between the straight line segment and the curve segment; finally, according to the input sequence of paired points of the active shaft and the driven shaft and the generated endpoint derivative values, according to customer needs, a cubic, quintic or septic Hermite interpolation function is constructed to transition between the points of the curve segment; S2: Hermite real-time interpolation operation: During the real-time interpolation operation, firstly, the sequence segment of the paired points of the active axis and the driven axis where the position is located is found according to the input real-time position of the active axis; then, according to the straight line-curve mixing coefficient, it is determined whether the active axis position adopts a straight line transition or a curve transition; if it is a straight line transition, the driven axis position will be obtained by straight line interpolation; if it is a curve transition, the driven axis position will be calculated according to the constructed Hermite interpolation curve.

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