CN101727089B - Method for correctly positioning clamp point by point - Google Patents

Abstract

The invention relates to a method for correctly positioning a clamp point by point, which is characterized by comprising the following steps: (1) determining theory constrained degrees of freedom according to processing requirements; (2) selecting a first positioning reference, and laying out a first positioning point on the selected positioning reference; (3) judging the correctness of the current positioning scheme, and if the positioning scheme belongs to full position, the positioning scheme is correct, finishing the design process; (4) if the positioning scheme is judged to belong to less positioning in step 3, returning to step 3; and (5) if the positioning scheme is judged to belong to less over positioning in step 3, returning to step 3. The invention is suitable for the analysis and design of the positioning schemes of workpieces with various structural shapes, can verify the feasibility of a prepared clamp positioning scheme, can correctly modify an existing clamp scheme, can determine the positioning reference, the number of the positioning points and the layout reasonably, and provides a theoretical basis for the development of a computer-aided clamp design system.

Description

Method for correctly positioning clamp point by point

Technical Field

The invention relates to a method for positioning a clamp, in particular to a method for correctly positioning a clamp point by point.

Background

To ensure that the machining, inspection, assembly, welding, etc. manufacturing process can be performed successfully, the workpiece must have a correct position and orientation relative to the tool. And the correct position and direction of the workpiece are realized by reasonably designing a positioning scheme of the clamp. Therefore, positioning solutions are one of the most important key issues in fixture design, both in the traditional manufacturing field and in modern flexible systems.

ASADA et al first established a kinematic model of a positioning scheme by using a Taylor expansion method, and used a full-rank Jacobian matrix of the kinematic model as a basis for judging unique positioning. CHOU et al established a clamping balance equation for prismatic workpieces using the spiral theory and concluded that the clamping spiral matrix for the clamping balance equation must be of full rank for the only sufficient condition for workpiece positioning. However, these research works have been discussed and described in detail with respect to only one particular form of logical positioning scheme (i.e., unique positioning).

KANG divides the positioning point layout into three types of complete positioning, under positioning and over positioning according to the relation between the number of the positioning points of the clamp and the number of the degrees of freedom restricted by the positioning points on the basis of the work of ASADA and the like. If the number of the positioning points is equal to the number of the degrees of freedom constrained by the positioning points and equal to 6, the positioning is complete; if the number of positioning points is more than the number of degrees of freedom constrained by the positioning points, the positioning points are under-positioned; and the number of anchor points less than the number of degrees of freedom constrained by itself is considered to be over-positioning. And the SONG et al perform detailed analysis on the positioning completeness according to the relation between the number of positioning points and the rank of the Jacobian matrix. If the rank of the Jacobian matrix is equal to 6 and the number of positioning points is also equal to 6, the workpiece is completely positioned; if the rank of the Jacobian matrix is equal to 6 and the number of the positioning points is more than 6, the workpiece is in an over-positioning state; if the rank of the Jacobian matrix is less than 6, then the workpiece is in an under-positioned state. In fact, these classification methods are not perfect. The rationality of the positioning scheme is not only related to the rank of the jacobian matrix but more importantly to the relationship between the theoretically constrained degrees of freedom and the practically constrained degrees of freedom.

Wu Zuguang et al propose an automatic determination algorithm of 3 positioning points on a side positioning reference in a 3-2-1 specific positioning scheme for a workpiece of which the positioning reference is composed of straight lines and circular arcs by using a link mechanism principle. However, this method is proposed under the assumption that the positioning of the workpiece is reasonable, and is suitable only for workpieces having a regularly shaped positioning reference surface.

Disclosure of Invention

The invention aims to provide a method for correctly positioning a clamp point by point, which is universal and effective, can ensure that a workpiece has a correct position and direction, and is suitable for complex workpieces with any shapes.

The invention is realized by dividing the positioning clamp into two different methods, one method is that a designer or a system autonomously finishes the design process of a positioning scheme according to the processing requirement without referring to the design result of any clamp case, and the method is characterized by comprising the following steps:

(1) determining theoretical constraint freedom according to processing requirements; (2) selecting a first positioning reference, wherein the positioning reference and the process reference are overlapped, and a first positioning point is arranged on the selected positioning reference; (3) judging the correctness of the current positioning scheme, if the positioning scheme belongs to full positioning, the positioning scheme is correct, and the design process is finished; (4) if the positioning scheme is judged to belong to under-positioning in the step 3, the number of the positioning points is not enough, a next positioning point is laid on the same positioning reference, and the step 3 is switched to; (5) if the positioning scheme is judged to be under-positioning in the step 3, the number of the positioning points is insufficient and the layout is not reasonable, a next positioning datum needs to be selected, a next positioning point is arranged on the positioning datum, and then the step 3 is carried out.

The other method is that firstly, aiming at a positioning scheme drawn up by designers according to experience and knowledge, the positioning correctness of the positioning scheme is analyzed, and then necessary editing and modification are carried out on similar clamps according to the processing requirements until the design process which can meet the processing requirements is realized, and the method comprises the following steps:

(1) analyzing the processing requirement, determining theoretical constraint freedom and calculating the minimum positioning point number; (2) judging the correctness of the current positioning scheme; (3) if the current positioning scheme is judged to be the only positioning or partial positioning in the step 2, the design process is finished; if the current positioning scheme belongs to under-positioning, selecting a first positioning reference, and adding a positioning point on the positioning reference surface to form a first positioning sub-scheme; (4) judging the correctness of the positioning sub-scheme, if the positioning sub-scheme belongs to full positioning, the positioning scheme is correct, and the design process is finished; (5) if the positioning sub-scheme is judged to be under-positioned in the step 4, selecting the next positioning reference, resetting the positioning point to form the next positioning sub-scheme, and returning to the step 4; if the positioning sub-scheme is judged to belong to under-positioning, adding a next positioning point on the positioning reference to form a next positioning sub-scheme, and returning to the step 4; (6) if the current positioning scheme is judged to be under-positioning in the step 2, selecting a first positioning reference to form a first positioning sub-scheme; (7) analyzing the correctness of the positioning sub-scheme; (8) if the current positioning sub-scheme is judged to be under-positioning in the step 7, reducing a positioning point on the current positioning reference, and returning to the step 7; if the current positioning scheme is judged to be under-positioned, selecting the next positioning reference to form the next positioning sub-scheme, judging that the positioning sub-scheme is not the last positioning sub-scheme, returning to the step 7, otherwise, adding a first positioning point on the first positioning reference to form the first positioning sub-scheme again; (9) analyzing the correctness of the current positioning scheme, if the current positioning scheme belongs to full positioning, the positioning scheme is correct, and the design process is finished; (10) if the current positioning scheme is judged to be under-positioned in the step 9, the positioning point is reset on the next positioning reference to form a next positioning sub-scheme, and the step 9 is returned; if the current positioning scheme belongs to under-positioning, adding a next positioning point to form a next positioning sub-scheme, and returning to the step 9; (11) if the current positioning scheme is judged to be the only over-positioning or the partial over-positioning in the step 2, selecting a first positioning reference to form a first positioning sub-scheme; (12) analyzing the correctness of the positioning sub-scheme; (13) if the positioning scheme judged in the step 12 belongs to over-positioning, reducing a positioning point on the current positioning reference, and returning to the step 12; (14) if the positioning scheme judged in the step 12 belongs to under-positioning, selecting the next positioning reference to form the next positioning sub-scheme, and returning to the step 12; (15) if the positioning scheme judged in step 12 belongs to full positioning, the design process is ended.

The two clamp positioning schemes are arranged point by pointIn the calculation process, there are two bases for judging the correctness of the positioning scheme: one is the theoretical condition k ═ k_minAnd the other is the process conditions rank (j) ═ k. Wherein k is_min6-rank (xi) is the minimum number of positioning points needed by a correct positioning scheme, and xi is all standard orthogonal bases in the theoretical constrained freedom; k' ═ rank (J) -rank (J ξ) is the number of valid positioning points, and k is the number of actual positioning points in the positioning scheme.

In the above two fixture positioning schemes point-by-point design algorithm flow, the method for judging the correctness of the positioning scheme is as follows:

(1) if k' < k_minAnd rank (j) ═ k, the positioning scheme is called under-positioning;

(2) if k' < k_minAnd rank (J) < k, the positioning scheme is called under-positioning;

(3) if k ═ k_minRank (J) < k and rank (J) < 6, the positioning scheme is called partial over-positioning;

(4) if k' is k_minAnd rank (j) 6 < k, then the positioning scheme is called the only over-positioning;

(5) if k ═ k_minAnd rank (j) ═ k, then the positioning scheme is called full positioning; in particular, when k is 6, such full positioning is referred to as unique positioning; and when k < 6, this full positioning is called partial positioning.

By utilizing the speed synthesis principle of particle motion, a freedom degree constraint model and a positioning scheme model are respectively established (modern design method of machine tool fixture, Beijing aviation industry publishing Co., Ltd.), and the final result is as follows:

1. a freedom degree constraint model delta r is established_P＝Eδq_wAnd δ r_PO＝Zδq_wThe establishment of the model describes the quantitative relation between the workpiece processing requirement and the theoretical constraint freedom degree. Wherein, <math> <mrow> <mi>&delta;</mi> <msub> <mi>q</mi> <mi>w</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>[</mo> <mi>&delta;</mi> <msubsup> <mi>r</mi> <mi>w</mi> <mi>T</mi> </msubsup> <mo>,</mo> <mi>&delta;</mi> <msubsup> <mi>&Theta;</mi> <mi>w</mi> <mi>T</mi> </msubsup> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math> the degrees of freedom are limited for theory; delta r_P＝[δx_P，δy_P，δz_P]^TThe variable quantity of the processing size or the positioning position of the workpiece is obtained; delta r_PO＝[δx_PO，δy_PO,δz_PO]^TThe variation of the orientation position of the workpiece; e ═ I^T，Ω^T]And I is a unit matrix, omega ═ r_PX is an obliquely symmetric matrix, r_P＝[x_P，y_P，z_P]^TThe position of any point P on the part; z ═ O^T，Ω^T]And O is a zero matrix.

2. A mathematical model of the positioning principle is established as <math> <mrow> <mi>J&delta;</mi> <msubsup> <mi>q</mi> <mi>w</mi> <mi>h</mi> </msubsup> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mrow> </math> The establishment of the model describes the quantitative relationship between the positioning solution and the actual constrained degrees of freedom. Wherein, $J={[J_1^T,J_2^T,...,J_k^T]}^T$ to locate the Jacobian matrix, an <math> <mrow> <msub> <mi>J</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mo>[</mo> <msubsup> <mi>n</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mo>,</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mi>i</mi> </msub> <mo>&times;</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>w</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>]</mo> <mo>;</mo> </mrow> </math> <math> <mrow> <mi>&delta;</mi> <msubsup> <mi>q</mi> <mi>w</mi> <mi>h</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mi>&delta;</mi> <msubsup> <mi>r</mi> <mi>w</mi> <mi>h</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>,</mo> <msup> <mrow> <mo>(</mo> <mi>&delta;</mi> <msubsup> <mi>&Theta;</mi> <mi>w</mi> <mi>h</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>]</mo> </mrow> <mi>T</mi> </msup> </mrow> </math> A degree of freedom that is practically limited for positioning schemes.

The invention has the advantages that: (1) the method is suitable for analyzing and designing positioning schemes of workpieces with various structural shapes; (2) the feasibility of the proposed fixture positioning scheme can be verified; (3) the existing clamp scheme can be corrected correctly; (4) the positioning reference, the number of positioning points and the layout thereof can be reasonably determined; (5) provides theoretical basis for the development of a computer-aided clamp design system.

Drawings

FIG. 1 is an exemplary illustration of a prismatic cylindrical workpiece and a processing surface according to the present invention;

FIG. 2 is an example diagram of adding a first positioning point to a first positioning datum of a prismatic-column workpiece according to the present invention;

FIG. 3 is an example diagram of adding a second positioning point to a first positioning datum of a prismatic-column workpiece according to the present invention;

FIG. 4 is an example diagram of adding a third positioning point to the first positioning datum of the prismatic-column workpiece according to the present invention;

FIG. 5 is an example diagram of adding a fourth positioning point to the first positioning datum of a prismatic-column workpiece according to the present invention;

FIG. 6 is a diagram of an embodiment of the present invention for resetting a fourth positioning point on a second positioning datum of a prismatic-pillar workpiece;

FIG. 7 is an example diagram of adding a fifth positioning point to the second positioning datum of the prismatic-column workpiece according to the present invention;

FIG. 8 is an example of a "4-2-1" positioning solution without slots of the present invention;

FIG. 9 is a diagram of a revised example of a first positioning sub-scheme of the invention without slots;

FIG. 10 is a modified example of the first out-of-slot detent sub-scheme of the present invention;

FIG. 11 is a diagram of a second embodiment of a non-slotted locator solution of the present invention before modification;

FIG. 12 is a modified example of a second out-of-slot positioning sub-scheme in accordance with the present invention;

FIG. 13 is a diagram of a third embodiment of a blind slot locator of the present invention;

FIG. 14 is an example of adding a positioning point 8 to a first positioning reference without a through groove according to the present invention;

FIG. 15 is a diagram illustrating an example of resetting the positioning point 8 on the second positioning reference without slots according to the present invention;

Detailed Description

The specific application of the point-by-point design algorithm in the design process of the positioning scheme is illustrated through a specific embodiment, and xi is recorded_x＝[1，0，0，0，0，0]^T、ξ_y＝[0，1，0，0，0，0]^T、ξ_z＝[0，0，1，0，0，0]^T、ξ_α＝[0，0，0，1，0，0]^T、ξ_β＝[0，0，0，0，1，0]^TAnd xi_γ＝[0，0，0，0，0，1]^TA set of orthonormal bases representing a six-dimensional space. The "generative" and "revised" design algorithms of the present invention are described in further detail below with reference to the accompanying drawings and examples, respectively.

Example 1:

the workpiece is assumed to be a regular prism, as shown in fig. 1. The surface to be machined is a step surface, and machining sizes a and b are required to be guaranteed. Therefore, the most critical link in the machining process is to reasonably design a positioning scheme so as to determine the correct position and direction of the workpiece relative to the cutter. The design process of the positioning scheme is detailed as follows:

step 1: in order to guarantee the machining dimensions a, b in the X and Y directions simultaneously, the degree of freedom δ q is theoretically constrained_wXi λ, where the base vector xi is xi_zArbitrary number vector λ ═ λ_zThus having k_min＝5；

Step 2: since the lower surface of the workpiece is the process datum, the surface is selected as the first positioning datum, and the first positioning point is laid out, as shown in FIG. 2,

and step 3: the jacobian matrix J is calculated as [0, -1, 0, -z₁，0，x₁]Thus, rank (J) ═ 1, rank (J ξ) ═ 0, so k' < k_min；

And 4, step 4: according to k' < k_minAnd rank (j) ═ k, it can be known that the positioning scheme belongs to the under-positioning mode, and is an unreasonable positioning scheme, and it can be known that the effective number of positioning points is not enough, so that a second positioning point should be laid out on the same positioning reference, as shown in fig. 3,

and 5: recalculating the Jacobian matrix $J=\left[\begin{array}{cccccc}0& -1& 0& -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& -z_2& 0& x_2\end{array}\right],$ Thus, rank (J) ═ 2, rank (J ξ) ═ 0, so k' < k_min；

Step 6: according to k' < k_minAnd rank (j) ═ k, it can be known that the positioning scheme still belongs to under-positioning, so the third positioning point is continuously laid out on the first positioning reference, as shown in fig. 4,

and 7: at this time $J=\left[\begin{array}{cccccc}0& -1& 0& -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& -z_2& 0& x_2\\ 0& -1& 0& -z_3& 0& x_3\end{array}\right],$ Thus rank (J) ═ 3, rank (J ξ) ═ 0, so k' < k_min；

And 8: the positioning scheme at this time still belongs to under-positioning, and for this reason, a fourth positioning point, i.e. k is 4, is added to the first positioning reference, as shown in fig. 5,

and step 9: continuing to compute the Jacobian matrix for the positioning solution $J=\left[\begin{array}{cccccc}0& -1& 0& -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& -z_2& 0& x_2\\ 0& -1& 0& -z_3& 0& x_3\\ 0& -1& 0& -z_4& 0& x_4\end{array}\right],$ For this reason, rank (J) ═ 3 and rank (J ξ) ═ 1 are readily known, so k' < k_min，rank(J)＜k；

Step 10: according to k' < k_minAnd rank (J) < k, the positioning scheme at this time is under-positioning, and the number of positioning points is not enough and the layout is not reasonable. Therefore, the left side surface is selected as the second positioning reference according to the reference superposition principle, and the fourth positioning point is laid out on the newly selected positioning reference, as shown in fig. 6;

step 11: calculating a Jacobian matrix for a positioning scheme as shown in the figure $J=\left[\begin{array}{cccccc}0& -1& 0& -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& -z_2& 0& x_2\\ 0& -1& 0& -z_3& 0& x_4\\ -1& 0& 0& 0& z_4& -y_4\end{array}\right],$ Thus, rank (J) ═ 4, rank (J ξ) ═ 0, so k' < k_min；

Step 12: according to k' < k_minAnd rank (j) ═ k, it can be known that the positioning scheme is under-positioned, obviously the number of positioning points is not enough, so the fifth positioning point is continuously laid out on the second positioning reference, as shown in fig. 7;

step 13: calculating the Jacobian matrix of the positioning scheme of FIG. 9 as $J=\left[\begin{array}{cccccc}0& -1& 0& {-\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& {-z}_2& 0& x_2\\ 0& -1& 0& {-z}_3& 0& x_3\\ -1& 0& 0& 0& z_4& {-y}_4\\ -1& 0& 0& 0& z_5& {-y}_5\end{array}\right],$ Therefore, rank (J) ═ 5, rank (J ξ) ═ 0, so k ═ k_min；

Step 14: according to if k ═ k_minAnd rank (j) ═ k, and k < 6, it can be known that the positioning scheme shown in fig. 9 is a partial positioning, which belongs to the correct positioning scheme. Therefore, the positioning scheme can determine the position and the direction of the workpiece relative to the cutter, so that the requirement of machining precision can be ensured;

example 2:

in order to obtain the design dimension a, b, h requirements of the blind groove, a workpiece and a cutter in the machining process must be reasonably determined firstly

Relative position therebetween. For this purpose, the "4-2-1" positioning scheme shown in FIG. 8 is adopted, and is analyzed in detail and modified correctly, as follows:

step 1: in order to simultaneously obtain design dimensions a, h and b in three directions, the degree of freedom delta q is theoretically constrained_wAnd the base vector xi is 0. Thus the minimum number of anchor points k_min＝6；

Step 2: as can be seen from FIG. 13The number k of the positioning points in the positioning scheme is 7, and the Jacobian matrix is easy to calculate $J=\left[\begin{array}{cccccc}0& -1& 0& {-\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& {-z}_2& 0& x_2\\ 0& -1& 0& {-z}_3& 0& x_3\\ 0& -1& 0& {-z}_4& 0& x_4\\ -1& 0& 0& 0& z_5& {-y}_5\\ -1& 0& 0& 0& z_5& -y_6\\ 0& 0& -1& y_7& {-x}_7& 0\end{array}\right],$ Thus, rank (J) ═ 5, rank (J ξ) ═ 0, so k' ═ 5;

and step 3: according to k' < k_minAnd rank (J) < k indicates that the positioning scheme belongs to under-over positioning, is an unreasonable positioning scheme, and indicates that the effective number of positioning points is insufficient and the layout is unreasonable;

and 4, step 4: in the positioning scheme in fig. 8, according to the importance of the positioning datum, decomposing into a plurality of positioning sub-schemes, first selecting a first positioning datum (i.e. the lower surface of the workpiece) and forming a first positioning sub-scheme by using the positioning points laid out on the first positioning datum, as shown in fig. 9, since in this positioning sub-scheme, k is 4, and rank (j) is 3, rank (j) (-3) < k (═ 4), one positioning point is removed from the first positioning datum, and it is assumed that the positioning point 4 is removed, as shown in fig. 10;

and 5: since rank (3) (═ k) (═ 3) in the positioning scheme shown in fig. 10, the second positioning reference and the positioning points laid out thereon are further added to form a second positioning sub-scheme, as shown in fig. 11, k ═ 5 and rank (j) (-4) are analyzed and calculated, so rank (j) (-4) < k (═ 5). Thus removing an anchor point on the second anchor point, assuming anchor point 6 is removed, as shown in fig. 12;

step 6: since rank (j) (4) ═ k) (═ 4) in the positioning scheme shown in fig. 12, the third positioning reference and the positioning points laid out thereon are further added and selected to form a third positioning sub-scheme, and rank (j) ((5) (═ 5) is analyzed and calculated as shown in fig. 13;

and 7: since the third positioning reference is the last positioning reference, the first positioning point, positioning point 8 in fig. 14, is added to the first positioning reference, and since the number of effective positioning points k' is 5, the number of minimum positioning points k is the number of minimum positioning points k_min6, and rank (j) < k (═ 6).

And 8: the anchor point 8 should be reset on the second positioning reference, as shown in fig. 15, when the anchor point 8 and the anchor point 5 have the same Y-coordinate, rank (j) 6, so that the number of effective anchor points k' 6 is due to the minimum number of anchor points k_min6, so k ═ k_minAnd, the design process ends.

Claims (1)

1. A method for correctly positioning a clamp point by point is characterized by comprising two point-by-point design algorithms:

the first point-by-point design algorithm comprises the following steps: (1) analyzing the processing requirement, determining theoretical constraint freedom and calculating the minimum positioning point number; (2) selecting a first positioning reference, and then laying out a first positioning point on the selected positioning reference; (3) judging the correctness of the current positioning scheme, if the positioning scheme belongs to full positioning, the positioning scheme is correct, and the design process is finished; if the positioning points belong to under positioning, the number of the positioning points is not enough, and the step 4 is executed; if the positioning is insufficient, the number of the positioning points is insufficient and the layout is not reasonable, and the step 5 is executed; (4) laying out a next positioning point on the same positioning reference, and executing the step 3; (5) deleting the previous positioning point, then selecting the next positioning reference, laying out the next positioning point on the positioning reference, and then turning to the step 3;

the second point-by-point design algorithm comprises the following steps: (1) analyzing the processing requirement and determining the theoretical constraint freedom degree delta q_wAnd calculating the minimum number k of location points_minBase vector xi, actual positioning point number k, effective positioning point number k', rank (J) and rank (J xi) of the Jacobian matrix of the positioning scheme; (2) judging the correctness of the current positioning scheme, and if the positioning scheme is the only positioning or partial positioning and the positioning scheme is correct, finishing the design process; if the current positioning scheme belongs to under-positioning, executing the step 3; if the current scheme belongs to under-positioning, executing the step 6; if the positioning belongs to the only over positioning or the partial over positioning, executing the step 10; (3) selecting a first positioning datum for analysis, adding a positioning point on the positioning datum plane, and taking the positioning point and other positioning points on the datum plane as an independent positioning sub-scheme; (4) calculating the number k 'of effective positioning points of the positioning sub-scheme'₀K 'if'₀＝k_minIf so, the positioning scheme is correct, and the design process is finished; k's'₀＜k_minIf yes, executing step 5; (5) judging the relationship between the rank of the Jacobian matrix and the number of the positioning points, if rank (J) is k, laying out the next positioning point on the newly added surface of the current positioning sub-scheme, updating the scheme into the positioning sub-scheme, and executing the step 4; if rank (J) < k, deleting the newly added positioning point, adding the next positioning datum, adding a positioning point on the positioning datum, using the positioning point on the datum and the previous datum as an updated positioning sub-scheme, and executing the step 4; (6) selecting a first positioning reference, and taking a positioning point on the reference as a positioning sub-scheme; (7) judging the relation between the rank (J) of the Jacobian matrix in the positioning sub-scheme and the number k of the positioning points, and if rank (J) is less than k, executing the step 8; if rank (j) ═ k, perform step 9; (8) reducing a positioning point on the positioning reference newly added at present, and updating the positioning referenceThe scheme is a positioning sub-scheme, and step 7 is executed; (9) adding a next positioning reference on the basis of the current positioning sub-scheme, updating the scheme into the positioning sub-scheme, judging whether the positioning sub-scheme is consistent with the current positioning scheme, and if so, executing the step 3; if not, executing step 7; (10) selecting a first positioning reference, and taking a positioning point on the reference as a positioning sub-scheme; (11) analyzing the relationship between the rank of the Jacobian matrix and the number of the positioning points in the positioning sub-scheme, and if rank (J) < k, executing step 12; if rank (j) ═ k, go to step 13; (12) deleting a positioning point on the positioning reference which is newly added at present, updating the scheme into a positioning sub-scheme, and executing the step 11; (13) calculating the number k 'of effective positioning points of the positioning sub-scheme'₀K 'if'₀＝k_minIf so, the positioning scheme is correct, and the design process is finished; k's'₀＜k_minThen go to step 14; (14) and adding the next positioning reference on the basis of the original positioning sub-scheme, updating the scheme into the positioning sub-scheme, and executing the step 11.

Images