Trajectory planning method for circular braiding traction robot considering yarn interaction

Abstract

The present invention relates to a circular weaving traction robot arm trajectory planning method that takes into account yarn interactions. The core shaft is segmented and divided into several weaving units, and the corresponding traction robot arm terminal motion trajectory when weaving on each core shaft unit is solved separately. Specifically, first, a mechanical analysis is performed on the interaction between the yarns in the convergence zone to determine the real-time state of the yarn after flexible deformation; then, the real-time convergence zone length when weaving on the current core shaft unit is calculated based on the flexible deformation of the yarn; and then the trajectory of the traction robot arm is planned based on the calculated real-time convergence zone length and the spatial geometric relationship between the core shaft unit and the weaving plane. The present invention can perform terminal trajectory planning for the robot arm used for traction of the core shaft in circular weaving on the basis of considering yarn interactions, so that the actual weaving angle of the circular weaving product is close to the expected target.

Description

Technical Field

[0001] The present invention relates to a trajectory planning method for an annular braiding traction robot arm, in particular to a trajectory planning method for an annular braiding traction robot arm considering yarn interaction, and belongs to the technical field of textile weaving. Background Art

[0002] Circular braiding is a process for producing seamless tubular fabrics. The braided yarns are drawn from two sets of spools, rotating clockwise and counterclockwise, respectively. As the spools rotate, the yarns intertwine and gradually deposit onto the moving mandrel to form the fabric. With the assistance of resin infusion technology, fabrics formed from chemical fiber yarns can be made into fiber-reinforced composite components. By varying the geometry of the mandrel, hollow components of varying shapes can also be obtained. Due to the mechanical properties of high-performance fabrics produced through circular braiding, these composite materials have been widely used in aviation, aerospace, automotive, shipbuilding, and other fields.

[0003] The orientation of the yarns in circularly woven fiber-reinforced composite components determines their geometric structure, which in turn has a significant impact on their mechanical properties. The braiding angle is a key parameter that characterizes the orientation of the yarns. Therefore, before performing circular braiding, it is necessary to determine the end trajectory of the robotic arm used for the mandrel based on the expected braiding angle of the composite braided component to be produced, in order to ensure that the braided component has the expected mechanical properties. In traditional methods, this trajectory is determined based on an ideal kinematic analysis of the spatial relationship in which the centerline of the mandrel is perpendicular to the plane where the braiding machine guide ring is located. However, when the centerline of the mandrel is non-straight, braiding using the trajectory obtained by the traditional method will result in the mandrel centerline not always being perpendicular to the braiding plane. The interaction between the yarns will also affect the length of the convergence zone, thereby causing a braiding angle error.

[0004] Therefore, in order to improve the above problems, it is necessary to provide an innovative circular braiding traction robot arm trajectory planning method that takes into account yarn interaction. Based on the analysis of the interaction between yarns, the real-time convergence zone length during weaving is calculated, and the real-time weaving plane is determined according to the convergence zone length. The traction robot arm trajectory is planned by ensuring that the center line of the core shaft is perpendicular to the weaving plane to overcome the defects of the existing technology. Summary of the Invention

[0005] In order to improve the above problems, the purpose of the present invention is to provide a circular braiding traction robot arm trajectory planning method that takes into account yarn interaction. In the process of planning the circular braiding traction robot arm trajectory, the method fully considers the influence of yarn interaction on the length of the convergence zone, thereby significantly reducing the gap between the fabric braiding angle and the expected target.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] A trajectory planning method for a circular braiding traction robot arm considering yarn interactions comprises the following steps:

[0008] (1) The pulled mandrel is divided into N mandrel units in the axial direction. The center points of the starting and ending end faces of each unit are taken respectively to obtain N+1 mandrel center points and N segments of mandrel center lines. In each unit, the mandrel center line is regarded as a straight line;

[0009] (2) Given a yarn quantity of 2m, with m warp and weft yarn quantities respectively, set the initial landing point P1 of each yarn and its contact point Q1 with the guide ring, and determine the subsequent landing point P of each yarn on any k-th core shaft unit according to kinematic analysis. k and its contact point Q with the guide ring k ;

[0010] (3) For each yarn P k and Q k Establish the equation of the line P k Q k , and determine the action points of warp and weft in the convergence area; for a certain warp yarn, compare it with the P of all weft yarns respectively k Q k The equations are combined into a system of m equations. If there is a solution within the convergence area, it is saved as an action point X i ;

[0011] (4) Calculate the X at each action point of each yarn under the ideal kinematic model. i The deflection angle γ after deformation due to interaction i '; For a certain warp yarn, it generates n action points with all m weft yarns in the convergence area. The mechanical analysis is used to determine the warp yarn at each action point X. i The deflection angle γ after deformation due to interaction i ';

[0012] (5) According to each yarn at each action point X i The deflection angle γ after deformation due to interaction i ', calculate the actual convergence zone length H of the yarn corresponding to the yarn when it is woven on the current k-th core shaft unit k ;

[0013] (6) The actual convergence zone length H corresponding to the weaving of all 2m yarns on the current k-th core unit k Take the average value and take it as the final actual converging zone length H on the mandrel unit. k ;

[0014] (7) Repeat steps (3) to (6) to calculate the actual convergence zone length when weaving on each core shaft unit;

[0015] (8) According to the N actual convergence zone lengths obtained on all N core shaft units, a coordinate system is established, and based on the change in the convergence zone length and the spatial geometric relationship that the core shaft center line is always perpendicular to the braiding plane, the end trajectory of the robotic arm used to pull the core shaft is calculated.

[0016] Furthermore, the mechanism used for circular braiding includes a winding mechanism, a core shaft, yarn, a spool, a guide ring, and a spool track disk; the expected braiding angle of the target fabric is set to α, the corresponding equivalent braiding angle is α', the spool rotation angular velocity is ω, the guide ring radius is R, the core shaft radius is r, the point where the yarn and the guide ring contact is Q, the point where the yarn and the core shaft contact is the landing point P, the actual distance from the yarn landing point to the guide ring, that is, the length of the convergence zone is H, the corresponding convergence zone length under the ideal kinematic model is H', and the contact point where the yarns interact is X i , the yarn is at the contact point X i The deflection angles before and after the deflection due to interaction are γ i and γ i ', the yarn is at the action point X i The angle θ produced relative to the mandrel surface is i , point of action X i The corresponding rotation angle in space is β i , point of action X i The gravity of the yarn segments on both sides is G i .

[0017] Furthermore, in the step (2), the yarn landing point for starting weaving on the k-th core shaft unit and its contact point with the guide ring are P and k and Q k , P k The rotation angle in the coordinate system is C s is the center point of the sth mandrel, Q k The rotation angle in the coordinate system is The first contact point Q1 is determined, that is Known, the contact point Q for starting weaving on any k-th core shaft unit is k Corner for:

[0018]

[0019] Where ± is + when the yarn is warp and - when the yarn is weft; then the contact point Q between the yarn and the guide ring on the kth core shaft unit is k Coordinates in the coordinate system for:

[0020]

[0021] When braiding, the yarn is tangent to the core surface. and The following relationship exists:

[0022]

[0023] Among them, ± is - when the yarn is warp yarn, and + when the yarn is weft yarn; then when weaving starts on the kth core shaft unit, the yarn landing point P k Coordinates in the coordinate system for:

[0024]

[0025] At this point, the coordinates of the yarn landing point and the coordinates of the contact point with the guide ring when weaving starts on all N core shaft units are obtained.

[0026] Furthermore, in step (4),

[0027] For each yarn’s n action points, at the current action point X i The obtained γ' is the next action point X i+1 γ at , that is:

[0028] γ i+1 =γ i ' (10)

[0029] Therefore, the expected braiding angle α is equal to the local braiding angle γ1 at the beginning of the yarn, and the equivalent braiding angle α' is equal to the local braiding angle γ at the end of the yarn. n ',Right now:

[0030]

[0031] Furthermore, in step (5), the actual convergence zone length H of a single yarn corresponding to the k-th core unit when weaving is performed k The calculation formula is:

[0032] H k =|P k X1|cosα+|X1X2|cosγ1'+|X2X3|cosγ2'+…+|X n Q k |cosα' (12).

[0033] Furthermore, in step (8), the coordinate system takes the center of the guide ring as the origin O, takes the xOy plane parallel to the ground, and the core shaft extraction direction is the y direction; the first section C0C1 of the core shaft centerline, the y direction of the core shaft coordinate system, and the axial direction of the guide ring coincide with each other, and the first center point C0 of the core shaft is located at the origin O of the core shaft coordinate system, that is, the position at a distance H1 in front of the center of the guide ring.

[0034] Furthermore, after the braiding traction machine is started, each motion trajectory of the end of the robotic arm must meet the following requirements:

[0035] 1) When weaving starts on the kth pancake-shaped core shaft unit, the center point C of the starting end face of the core shaft unit k-1 The distance from the center of the guide ring is the actual convergence zone length H in real time. k ;

[0036] 2) When weaving starts on the kth pancake-shaped core shaft unit, the center line C of the core shaft unit k-1 C k Perpendicular to the real-time weaving plane.

[0037] Compared with the prior art, the present invention has the following beneficial effects: the circular weaving traction robot arm trajectory planning method considering yarn interaction of the present invention can calculate the traction robot arm trajectory required for producing fabrics with specified weaving angles through circular weaving for a core shaft with a straight or non-straight center line, thereby reducing the gap between the weaving angle of the fabric product and the expected target and improving production quality and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the circular knitting in the present invention.

[0039] Figure 2 It is a schematic diagram of the robotic arm in the present invention.

[0040] Figure 3 It is an analytical model diagram of a single yarn in the present invention.

[0041] Figure 4 It is a schematic diagram of the relative positions of the yarn and the core shaft in the present invention.

[0042] Figure 5 This is a diagram for analyzing the derivation of the deformation angle of a single yarn in the present invention.

[0043] Figure 6 The single yarn in the present invention is at the point of action X i Force analysis diagram.

[0044] Figure 7 is the action point X in the present invention i Schematic diagram of spatial location.

[0045] Figure 8Schematic diagram of yarn unit deformation in the present invention.

[0046] Figure 9 It is a schematic diagram of the initial position of the core shaft in the present invention.

[0047] Figure 10 It is a schematic diagram of the translational motion of the core shaft in the present invention.

[0048] Figure 11 It is a schematic diagram of the rotational motion of the core shaft around the x-axis in the present invention.

[0049] Figure 12 It is a schematic diagram of the rotational motion of the core shaft around the z-axis in the present invention.

[0050] Figure 13 This is a flow chart of the trajectory planning method of a circular braiding traction robot arm considering yarn interactions of the present invention. DETAILED DESCRIPTION

[0051] In order to make the technical solution of the present invention clearer, the following further describes the implementation methods of the present invention in conjunction with the accompanying drawings and examples. The description of the specific implementation methods can make the technical problems solved by the present invention, the technical solutions adopted, and the technical effects achieved more clearly explained. It is understood that the specific embodiments described herein are only used to more clearly explain the present invention, rather than to limit the present invention. It should also be noted that, for the convenience of description, the accompanying drawings only show the parts related to the present invention, not all of the contents, and cannot be used to limit the scope of protection of this application.

[0052] The present invention will be described in detail below with reference to the accompanying drawings. Unless there is any conflict, the features of the following embodiments and implementations may be combined with each other.

[0053] like Figure 1 As shown, the object of the present invention is a core shaft with a straight or non-straight center line ( Figure 1 The circular braiding machine (taking the straight centerline core shaft section as an example) is mainly composed of a winding mechanism 1, a core shaft 2, a yarn 3, a bobbin 4, a guide ring 5 and a bobbin track disk 6. The winding mechanism 1 is as follows Figure 2 The end of the robotic arm shown is responsible for grabbing the mandrel and pulling it to the left. Two sets of bobbins 4 rotate clockwise and counterclockwise around the center of the bobbin track 6. The left end of yarn 3 is fixed to the left end of mandrel 2, while the right end of yarn 3 is wound around the two sets of bobbins 4. Therefore, yarn 3 also moves clockwise and counterclockwise as the bobbins rotate.

[0054] In the analysis, the present invention simplifies it as follows Figure 3The model shown. Assume that mandrel 2 moves leftward under the traction of the robotic arm, the expected braiding angle of the target fabric is α, the angular velocity of bobbin 4 is ω, the radius of guide ring 5 is R, the radius of mandrel 2 is r, the contact point between yarn 3 and guide ring 5 is Q, the contact point between yarn 3 and mandrel 2 is landing point P, and the distance from the landing point of yarn 3 to guide ring 5, i.e., the length of the convergence zone, is H. The yarns are densely distributed in the convergence zone, and friction and other interactions between them have a significant impact on the braiding process. The surface of guide ring 5 is relatively smooth, so factors such as the interactions between yarns 3 and their thickness are taken into consideration, while the friction between yarn 3 and guide ring 5 is ignored. As a result, the movement of bobbin 4 on bobbin track 6 and the movement of contact point Q between yarn 3 and guide ring 5 can be assumed to be synchronized. In other words, bobbin track 6 can be ignored in the model, and the angular velocity of contact point Q on guide ring 5 is also ω.

[0055] The input parameters required by the present invention include: core shaft winding speed v, yarn quantity 2m, angular velocity ω, target braiding angle α, guide ring radius R, and yarn tension T.

[0056] See also Figure 13 , the specific method of the present invention is as follows:

[0057] (1) A pulled mandrel is divided into N mandrel units in the axial direction according to a certain step length (the step length is related to the solution accuracy, generally 1 / 100 to 1 / 50 of the mandrel length). The center points of the start and end faces of each unit are taken respectively to obtain N+1 mandrel center points C0, ..., C N And N segments of mandrel centerline, in each unit, the mandrel centerline is regarded as a straight line. Figure 3 As shown, a spatial Cartesian coordinate system is established with the center of the guide ring as the origin and the axis of the core shaft as the z direction.

[0058] (2) Given a yarn quantity of 2m, with m warp (clockwise) and m weft (counterclockwise) yarn quantities, the initial drop point P1 of each yarn and its contact point Q1 with the guide ring are set according to production needs, and the subsequent drop point P of each yarn on any k-th core shaft unit is determined according to kinematic analysis. k and its contact point Q with the guide ring k .

[0059] Specifically, the two ends of 2m yarns (m warp yarns and m weft yarns) are the starting end face of the core shaft and the guide ring respectively. The yarn landing point starting from the kth core shaft unit and the contact point with the guide ring are P k and Q k , P k The rotation angle in the coordinate system is Q k The rotation angle in the coordinate system is s is a subscript, Cs That is the center point of the sth core axis (starting from the 0th). The first contact point Q1 is determined, that is Known, the contact point Q for starting weaving on any k-th core shaft unit is k Corner for:

[0060]

[0061] Where ± is + when the yarn is warp and - when the yarn is weft. Then the contact point Q between the yarn and the guide ring on the kth core shaft unit is k Coordinates in the coordinate system for:

[0062]

[0063] When braiding, the yarn is tangent to the core surface, such as Figure 4 As shown, and The following relationship exists:

[0064]

[0065] Where ± is - when the yarn is warp, and + when the yarn is weft. Then the yarn landing point P when weaving starts on the kth core shaft unit is k Coordinates in the coordinate system for:

[0066]

[0067] At this point, the coordinates of the yarn landing point and the coordinates of the contact point with the guide ring when weaving starts on all N core shaft units can be obtained.

[0068] (3) Next, calculate the actual convergence zone length H when starting to weave any k-th core shaft unit. k The contact point Q between the yarn and the guide ring at the current moment has been obtained k , the actual landing point P of the yarn on the core shaft at the current moment k . Connect each yarn's P separately k , Q k , we can get 2m P k Q k Equation of a straight line. For any warp yarn, change its P k Q k The equations are respectively related to the P of m weft yarns k Q k The equations are combined into m equations. If a system of equations has a solution within the convergence area, it is saved as an action point X. i, from which n solutions are obtained from the m sets of equations, that is, n action points of the warp yarn are obtained (n < m), and the same applies to the remaining (2m - 1) yarns.

[0069] (4) Next, calculate the actual convergence zone length corresponding to each of the 2m yarns under the influence of yarn - to - yarn interaction. As Figure 5 shown, for each warp yarn, Q k is its contact point with the guide ring, P k is the actual landing point of the yarn on the mandrel at the current moment, X1, X2, …, X n are the action points of the n weft yarns in contact with the warp yarn in the convergence zone, and the warp yarn is divided into n + 1 analysis units according to these n action points. In the ideal kinematic model, when ignoring the influence of yarn - to - yarn interaction in the convergence zone, the warp yarn remains in a straight line, as shown by P k 'Q k , forming a braiding angle α' and a convergence zone length H'; while the interaction causes the yarn to produce a certain bending deflection in the convergence zone during actual braiding, as shown by P k Q k , forming a braiding angle α and the actual convergence zone length H. Given the known expected braiding angle, that is, the actual braiding angle α, from P k to Q k , through the mechanical analysis of each yarn unit, the deflection angle γ i ' at each action point X i and the end - point angle α' of any yarn after flexible deformation can be obtained, creating conditions for subsequent calculation of the actual convergence zone length H.

[0070] The chemical fiber yarns used in circular braiding have the characteristics of high strength and high modulus, which means that when the yarns interact due to contact, they hardly produce axial deformation, but are mainly affected by the frictional force between the yarns. For each yarn unit of the current warp yarn, first analyze it in the plane perpendicular to the frictional force F, as Figure 6 shown. Considering the yarn volume, due to the interweaving with the weft yarn, the warp yarn generates an angle θ i at the action point X i relative to the surface of the mandrel, making the normal force W i include the combined action of the yarn tensions T on both sides and the gravity G i of the yarn unit itself:

[0071] W i = T(sinθ i + sinθ i+1 ) ± G i [[ID= fifty - one]]cosβ i (5)

[0072] where βi X is the point of action i The corresponding corner in space, such as Figure 7 As shown. Friction force F i By the normal force W i Determined by the extended form of the classical friction law:

[0073] F i =aW i l (6)

[0074] Where a and l are both empirical formula constants.

[0075] Now let’s talk about friction force F. i Analyze on the plane where Figure 8 As shown. Still in this yarn unit, the warp yarn to which it belongs moves under the traction of the bobbin moving at an angular velocity of -ω, and in the convergence area, it converges with the weft yarn moving in the opposite direction at the action point X. i Contact. Subject to friction force F i The influence of the warp in X i Flexible deformation occurs at the point where the deflection angle is changed from γ to γ ​​under the balance of forces. i becomes γ i '. The corresponding relationship is:

[0076]

[0077] Among them, F 合ω is the resultant force in the direction of rotation, F 合z is the axial force of the core shaft, T i =Tcosθ is the yarn tension T before yarn deformation under friction F i The component on the plane, T i ' is the yarn tension T under the friction force F after yarn deformation i The component on the plane, F i is the friction force, γ i is the local braiding angle before yarn deformation, γ i ' is the local braiding angle after yarn deformation.

[0078] Among them, T i is the yarn tension T in the friction force F i Components on the plane:

[0079] T i =T cosθ i (8)

[0080] Further from (3), we can deduce that γ i with γ i 'The relationship is:

[0081]

[0082] For each yarn’s n action points, at the current action point X i The obtained γ' is the next action point X i+1 γ at , that is:

[0083] γ i+1 =γ i ' (10)

[0084] Therefore, the expected braiding angle α is equal to the local braiding angle γ1 at the beginning of the yarn, and the equivalent braiding angle α' is equal to the local braiding angle γ at the end of the yarn. n ',Right now:

[0085]

[0086] (5) Thus, the X of each action point of any yarn after flexible deformation is obtained i The deflection angle γ i ' and the end angle α'. Based on this, the actual convergence zone length H of the yarn corresponding to the current k-th pancake core shaft unit can be obtained as follows: k :

[0087] H k =|P k X1|cosα+|X1X2|cosγ1'+|X2X3|cosγ2'+…+|X n Q k |cosα' (12)

[0088] (6) Similarly, the above analysis is performed on all 2m yarns on the current k-th pie-shaped core unit, and 2m corresponding H k , and take the average value as the actual convergence zone length H when weaving on the kth pancake core shaft unit k .

[0089] (7) Repeat steps (3) to (6) to obtain the actual convergence zone length H when weaving starts on all N core shaft units.

[0090] (8) Next, plan the end trajectory of the robot arm used to pull the mandrel. The weaving process on each pancake-shaped mandrel unit is a section of the end trajectory of the robot arm, and there are N+1 trajectory points, which are represented by TP0~TP N Indicates that each trajectory point has six-dimensional information (x, y, x, w, p, r), the first three items are position, and the last three items are attitude. A new trajectory description coordinate system is established, with the center of the guide ring as the origin O, the xOy plane parallel to the ground, and the core axis extraction direction as the y direction. The initial position of the core axis is as follows Figure 9As shown, the first segment of the mandrel centerline C0C1, the y-direction of the mandrel coordinate system, and the axial direction of the guide ring coincide with each other, and the first center point C0 of the mandrel is located at the origin O of the mandrel coordinate system, which is a distance H1 in front of the center of the guide ring. After the braiding traction machine is started, the following two points must be ensured for each segment of the motion trajectory of the robot end:

[0091] 1) When weaving starts on the kth pancake-shaped core shaft unit, the center point C of the starting end face of the core shaft unit k-1 The distance from the center of the guide ring is the actual convergence zone length H in real time. k ;

[0092] 2) When weaving starts on the kth pancake-shaped core shaft unit, the center line C of the core shaft unit k-1 C k Perpendicular to the real-time weaving plane.

[0093] For this purpose, take the general k-1 segment trajectory as an example, which corresponds to the knitting process on the k-1 pancake core shaft units, and the first and last trajectory points TP k-2 and TP k-1 are the trajectory points when weaving starts on the k-1th core shaft unit and the kth core shaft unit respectively. k-2 and TP k-1 The movement between the two is decomposed into three steps: First, the core shaft is translated so that the center point C of the starting end face of the kth core shaft unit after the movement k-1 The distance from the center of the guide ring is the actual convergence zone length H in real time. k , and at this time C k-1 The position where the core is located is the origin, and a temporary coordinate system is established in the same direction as the trajectory description coordinate system; then, the core shaft is rotated around the x-axis of the temporary coordinate system so that the center line C of the kth core shaft unit after movement k-1 C k Rotate to the xOy plane; finally, rotate the mandrel around the z-axis of the temporary coordinate system so that the center line C of the kth mandrel unit after movement k-1 C k Rotate to the yOz plane. Since the temporary coordinate system and the trajectory description coordinate system only differ in position but have the same direction, the posture information of the center point of the core shaft starting end face in the temporary coordinate system is recorded at this time, which is the posture information of the desired trajectory point in the trajectory description coordinate system.

[0094] In specific calculation, the distance of translational motion is determined by the center line C of the k-1th core axis unit. k-2 C k-1 and the change in the length of the convergence zone ΔH, using Represents any center point C k The coordinates of (x c ,y c ,zc ) and (x c,new ,y c,new ,z c,new ) uniformly represents the coordinates of all center points before and after each movement. After the translation movement, the new coordinates of all center points of the mandrel are:

[0095]

[0096] The change in the length of the convergence zone, ΔH, is:

[0097] ΔH=H k -H k-1 (14)

[0098] The position change of the center line of the core axis in the trajectory description coordinate system before and after translation is as follows: Figure 10 shown.

[0099] After the translation is completed, we analyze the rotation of the core shaft around the x-axis in the yOz plane. Figure 11 As shown, in the temporary coordinate system y'O'z', in order to make the center line C of the k-th core shaft unit k-1 C k Rotate to the xOy plane in space (projected to the y-axis in the yOz plane), and all the center points of the mandrel need to be rotated by an angle a1:

[0100]

[0101] When a1≤0, the rotation direction is counterclockwise and the angle is -a1; when a1>0, the rotation direction is clockwise and the angle is a1. That is, according to the right-hand rule, the attitude angle change of the core shaft around the x-axis is -a1. At the same time, according to the plane geometry relationship, after the rotation, the new coordinates of all the center points of the core shaft in the yOz plane are:

[0102]

[0103] After that, continue to analyze the rotation of the core shaft around the z axis on the xOy plane. Figure 12 As shown, in the temporary coordinate system x'O'y', in order to make the center line C of the k-th core shaft unit k-1 C k Rotate to the yOz plane in space (projected to the y-axis in the xOy plane), and all the center points of the mandrel need to be rotated by an angle a2:

[0104]

[0105] When a2>0, the rotation direction is counterclockwise, and the angle is a2; when a2≤0, the rotation direction is clockwise, and the angle is -a2. That is, according to the right-hand rule, the attitude angle change of the core shaft around the z-axis is a2. At the same time, according to the plane geometry relationship, after the rotation, the new coordinates of all the center points of the core shaft in the xOy plane are:

[0106]

[0107] It should be noted that after each movement, the coordinates of all center points (x c ,y c ,z c )Use the latest (x c,new ,y c,new ,z c,new )renew.

[0108] After the three-step motion is completed, the mandrel completes the k-1th pie-shaped mandrel unit from the trajectory point TP k-2 To TP k-1 At this time, the position of the first center point C0 of the mandrel is the k-1th trajectory point TP k-1 , let it be Among them, the position coordinates That is, the latest position coordinates (x c,new ,y c,new ,z c,new ), which has been obtained by equations (16) and (18), the following deduces its posture information

[0109] The k-2th trajectory point TP is known k-2 The posture information is In the analysis of the core shaft's rotational motion around the x-axis and the z-axis, we have obtained that the attitude angle changes of the core shaft rotating around the x-axis and the z-axis are -a1 and a2 respectively. Then TP k-2 The posture information can be used as the rotation matrix Expressed as:

[0110]

[0111] To simplify the representation, Replace them with (w,p,r) respectively.

[0112] The rotation of the core shaft around the x-axis and the z-axis can also be expressed using the rotation matrix T rot Expressed as:

[0113]

[0114] Then the k-1th trajectory point TPk-1 The rotation matrix representation of the posture information for:

[0115]

[0116] Next, you need to TP k-1 The rotation matrix representation of the posture information Converted into attitude angle representation set up The elements of are:

[0117]

[0118] Then the k-1th trajectory point TP k-1 attitude angle for:

[0119]

[0120] It should be noted that the range of the inverse tangent function arctan is (-π,π], which reflects the correct quadrant information.

[0121] So far, any k-1th trajectory point TP has been realized k-1 Pose information in the trajectory description coordinate system Derivation of . Given the position and centerline information of the first trajectory point TP0 and the core shaft, the integer k is taken in the interval [2, N+1]. The position information of all N+1 trajectory points in the trajectory description coordinate system can be derived, realizing the trajectory planning of the circular braiding core shaft pulling robot arm.

[0122] The above specific implementation methods are only preferred embodiments of this creation and are not intended to limit this creation. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this creation should be included in the scope of protection of this creation.

Claims

1. A trajectory planning method for a circular braiding traction robot considering yarn interactions, characterized in that: The steps include: (1) The pulled mandrel is divided into N mandrel units in the axial direction according to a certain step length. The center points of the starting and ending end faces of each unit are taken respectively to obtain N+1 mandrel center points and N segments of mandrel center lines. In each unit, the mandrel center line is regarded as a straight line; (2) Given a yarn quantity of 2m, with m warp and weft yarn quantities respectively, set the initial landing point of each yarn on the core shaft to P1 and its contact point with the guide ring to Q1, and determine the subsequent landing point P of each yarn on any k-th core shaft unit according to kinematic analysis. k and its contact point Q with the guide ring k ; (3) For each yarn P k and Q k Establish the equation of the line P k Q k , and determine the action points of the warp and weft yarns in the convergence area; for a certain warp yarn, compare it with the equations P of all weft yarns respectively k Q k The system is composed of m equations. If there is a solution within the convergence area, it is saved as an action point X. i ; (4) Calculate the X of each action point of each yarn under the ideal kinematic model i The deflection angle γ after deformation due to interaction i '; For a certain warp yarn, it generates n points of action with all m weft yarns in the convergence area, where n is less than m; For each yarn’s n action points, at the current action point X i The obtained γ i ' is the next action point X i+1 γ i+1 ,Right now: c i+1 =c i ' (10) Therefore, the expected braiding angle α of the target fabric is equal to the local braiding angle γ1 at the beginning of the yarn, and the equivalent braiding angle α' corresponding to α is equal to the local braiding angle γ at the end of the yarn. n ',Right now: (5) According to the deflection angle γ of each yarn i ', calculate the actual convergence zone length H of the yarn corresponding to the yarn when it is woven on the current k-th core shaft unit k ; H k =|P k X1|cosα+|X1X2|cosγ1'+|X2X3|cosγ2'+…+|X n Q k |cosα' (12); (6) The actual convergence zone length H corresponding to the weaving of all 2m yarns on the current k-th core unit k Take the average value and take it as the final actual converging zone length H on the mandrel unit. k - ; (7) Repeat steps (3) to (6) to calculate the actual convergence zone length when weaving on each core shaft unit; (8) establishing a coordinate system based on the N actual convergence zone lengths obtained on all N mandrel units, and calculating the trajectory of the end of the robotic arm used to pull the mandrel based on the change in the convergence zone length and the spatial geometric relationship that the mandrel centerline is always perpendicular to the braiding plane; The coordinate system takes the center of the guide ring as the origin O, takes the xOy plane parallel to the ground, and the core shaft extraction direction is the y direction; the first section C0C1 of the core shaft centerline, the y direction of the core shaft coordinate system, and the axial direction of the guide ring coincide with each other, and the first center point C0 of the core shaft is located at a position H1 in front of the origin O of the core shaft coordinate system, that is, the center of the guide ring; After the weaving traction is started, each motion trajectory of the end of the robotic arm must meet the following requirements: 1) When weaving starts on the kth core shaft unit, the center point C of the starting end face of the core shaft unit k-1 The distance from the center of the guide ring is the actual convergence zone length in real time 2) When weaving starts on the kth core unit, the center line C of the core unit k-1 C k Perpendicular to the real-time weaving plane.

2. The circular braiding traction robot arm trajectory planning method considering yarn interaction according to claim 1 is characterized in that: The mechanism used in circular braiding includes a winding mechanism, a core shaft, yarn, a spool, a guide ring and a spool track disk; the angular velocity of the spool is ω, the radius of the guide ring is R, and the radius of the core shaft is r.

3. The circular braiding traction robot arm trajectory planning method considering yarn interaction according to claim 2, characterized in that: In the step (2), P k The rotation angle in the coordinate system is C s is the center point of the sth mandrel, Q k The rotation angle in the coordinate system is The first contact point Q1 is determined, that is Known, the contact point Q for starting weaving on any k-th core shaft unit is k Corner for: Where v represents the winding speed of the core shaft, ± is + when the yarn is warp yarn, and - when the yarn is weft yarn; then the contact point Q between the yarn and the guide ring on the kth core shaft unit is k Coordinates in the coordinate system for: When braiding, the yarn is tangent to the core surface. and The following relationship exists: Among them, ± is - when the yarn is warp yarn, and + when the yarn is weft yarn; then when weaving starts on the kth core shaft unit, the yarn landing point P k Coordinates in the coordinate system for: At this point, the coordinates of the yarn landing point and the coordinates of the contact point with the guide ring when weaving starts on all N core shaft units are obtained.

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