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

The method of the correct positioning fixture of pointwise

Technical field

The present invention relates to a kind of method of positioning fixture, relate in particular to the method for the correct positioning fixture of a kind of pointwise.

Background technology

Can run succeeded in order to ensure process for making such as machine work, check, assembling, welding, workpiece must have a tram and a direction with respect to cutter.And the correct location of workpiece and direction are to realize through the targeting scheme of appropriate design anchor clamps.Therefore, no matter be in traditional manufacturing field or the modern flexible system, targeting scheme is of paramount importance key issue in the jig Design.

People such as ASADA utilize the Taylor expansion method, have set up the kinematics model of targeting scheme first, and with the full rank Jacobi matrix of the kinematics model basis for estimation as unique location.People such as CHOU then utilize screw theory, have set up the clamping balance equation of prismatic workpiece, and infer and think that the adequate condition of the unique location of workpiece is the necessary full rank of clamping spiral matrix of clamping balance equation.Yet these research work only go through and describe to a kind of special shape (being unique location) of Reasonable Orientation scheme.

KANG according to the relation between anchor clamps anchor point number and the degree of freedom number that retrained thereof, is divided into the anchor point layout fully and locatees, to owe the location, cross and locate three types on the basis of people such as ASADA work.If the anchor point number equals the degree of freedom number that himself retrains, and is equal to 6, then be location fully; If the anchor point number is more than degree of freedom number that himself retrained then for owing the location; The anchor point number is less than the degree of freedom number that himself retrains and then was considered to the location.People such as SONG have carried out labor then according to the relation between the order of anchor point number and Jacobi matrix to the location completeness.If the order of Jacobi matrix equals 6, and the anchor point number also equals 6, and workpiece is by location fully so; If the order of Jacobi matrix equals 6, and the anchor point number is greater than 6, and workpiece was in positioning states so; If the order of Jacobi matrix is less than 6, workpiece is in and owes positioning states so.In fact, these sorting techniques and imperfection.The rationality of targeting scheme is not only relevant with the order of Jacobi matrix, and the relation between the degree of freedom of what is more important and theory constraint degree of freedom and physical constraint is relevant.

People such as Wu Zu Guang utilize the linkage assembly principle, and to the workpiece of being made up of positioning reference straight line and circular arc, what proposed in " 3-2-1 " certain position scheme 3 anchor points on the positioning reference of side confirms algorithm automatically.Yet this method is located under the rational assumed condition at workpiece and is proposed, and only is suitable for having the workpiece on regular shape positioning reference surface.

Summary of the invention

The object of the present invention is to provide the method for the correct positioning fixture of a kind of pointwise, this method is general, effective, can guarantee that not only workpiece has correct position and direction, and be applicable to the complex part with arbitrary shape.

The present invention realizes like this; Positioning fixture divides two kinds of diverse ways; A kind of method is not with reference to the design result of any anchor clamps case, independently accomplishes the design process of targeting scheme by designer or system according to processing request, it is characterized in that method step is:

(1) confirms the theory constraint degree of freedom according to processing request; (2) select first positioning reference, positioning reference and operation benchmark should overlap, first anchor point of layout on selected positioning reference; (3) judge the correctness of current targeting scheme, if belong to full location, then targeting scheme is correct, and design process finishes; (4) if step 3 judge that targeting scheme belongs to and owe the location, then the anchor point number is not enough, should be on identical positioning reference the next anchor point of layout, and change step 3 over to; (5) if step 3 judge that targeting scheme belongs to and owed the location, then the anchor point number is not enough and layout is also unreasonable, then need select next positioning reference, and on this positioning reference the next anchor point of layout, change step 3 afterwards over to.

Another kind method for earlier to the designer rule of thumb, the targeting scheme drafted of knowledge; Analyze its location correctness; According to processing request similar anchor clamps are carried out necessary editor and modification then, until the design process that can satisfy processing request, method step is:

(1) analyzes processing request, confirm the theory constraint degree of freedom and calculate minimum location and count; (2) correctness of the current targeting scheme of judgement; (3) if it is unique location or part location that step 2 is judged current targeting scheme, then design process finishes; Owe the location if current targeting scheme belongs to, then select first positioning reference, and on this positioning reference plane, set up an anchor point, form first locator scheme; (4) correctness of judgement locator scheme, if the locator scheme belongs to full location, then targeting scheme is correct, design process finishes; (5) owed the location if step 4 judgement locator scheme belongs to, then selected next positioning reference, reseted this anchor point, and formed next locator scheme, and return step 4; Owe the location if judgement locator scheme belongs to, then on this positioning reference, set up next anchor point, form next locator scheme, and return step 4; (6) for owing the location, then select first positioning reference if step 2 is judged current targeting scheme, form first locator scheme; (7) correctness of analyzing and positioning subscheme; (8), then on current positioning reference, reduce by an anchor point, and return step 7 if step 7 is judged current locator scheme for owing the location; If judge that current targeting scheme is for owing the location; Then select next positioning reference, form next locator scheme, and judge that this locator scheme is not last locator scheme; Then return step 7; Otherwise, on first positioning reference, set up first anchor point, form first locator scheme again; (9) correctness of the current targeting scheme of analysis, if current targeting scheme belongs to full location, then targeting scheme is correct, design process finishes; (10) owed the location if the current targeting scheme of step 9 judgement belongs to, then on next positioning reference, reseted this anchor point, and formed next locator scheme, and return step 9; Owe the location if current targeting scheme belongs to, then set up next anchor point, form next locator scheme, return step 9; (11) judge that as if step 2 current targeting scheme is that the location is perhaps partly crossed in unique location of crossing, then select first positioning reference, form first locator scheme; (12) correctness of analyzing and positioning subscheme; (13), then on current positioning reference, reduce by an anchor point, and return step 12 if the targeting scheme that step 12 is judged belonged to the location; (14) owe the location if the targeting scheme that step 12 is judged belongs to, then select next positioning reference, form next locator scheme, return step 12; (15) if the targeting scheme that step 12 is judged belongs to full location, then design process finishes.

In two above-mentioned anchor clamps targeting scheme pointwise algorithm for design flow processs, the foundation of described judgement targeting scheme correctness has two: one is theoretical condition k '=k _Min, another is process conditions rank (J)=k.Wherein, k _Min=6-rank (ξ) is the required minimum anchor point number of correct targeting scheme, and ξ is all orthonormal basis in the theory constraint degree of freedom; K '=rank (J)-rank (J ξ) counts for effectively locating, and k is that the actual location in the targeting scheme is counted.

In two above-mentioned anchor clamps targeting scheme pointwise algorithm for design flow processs, the method for described judgement targeting scheme correctness is:

(1) if k '＜k _MinAnd rank (J)=k claims that then targeting scheme is for owing the location;

(2) if k '＜k _MinAnd rank (J)＜k claims that then targeting scheme was for owing the location;

(3) if k '=k _Min, rank (J)＜k and rank (J)＜6 claim that then targeting scheme is that part is crossed the location;

(4) if be k '=k _MinAnd rank (J)=6＜k claims that then targeting scheme is unique location of crossing;

(5) if k '=k _MinAnd rank (J)=k claims that then targeting scheme is full location; Especially, when k=6, this full location is referred to as unique location; And when k＜6, this full location is referred to as the part location.

Utilize the speed composition principle of particle movement, set up degree of freedom restricted model, targeting scheme model (" modern Design of jig ", Beijing aircraft industry publishing house) respectively, net result is:

1, having set up the degree of freedom restricted model is δ r _P=E δ q _wWith δ r _PO=Z δ q _w, the quantitative relationship of workpiece processing requirement with the theory constraint degree of freedom described in the foundation of this model.Wherein, $\mathrm{\δ}{q}_w={[\mathrm{\δ}{r}_w^T,\mathrm{\δ}{\mathrm{\Θ}}_w^T]}^T$ Be the one theory degree of freedom; δ r _P=[δ x _P, δ y _P, δ z _P] ^TVariable quantity for workpiece processing size or position location; δ r _PO=[δ x _PO, δ y _PO, δ z _PO] ^TVariable quantity for the workpiece orienting station; E=[I ^T, Ω ^T], and I is unit matrix, Ω=r _P* be skew matrix, r _P=[x _P, y _P, z _P] ^TPosition for any 1 P on the part; Z=[O ^T, Ω ^T], and O is a null matrix.

2, having set up the positioning principle mathematical model does $\mathrm{J\δ}{q}_w^h=0,$ The quantitative relationship between targeting scheme and the physical constraint degree of freedom has been described in the foundation of this model.Wherein, $J={[J_1^T,J_2^T,...,J_k^T]}^T$ Be the location Jacobi matrix, and $J_i=-[n_i^T,{(n_i\×r_i^w)}^T];$ $\mathrm{\δ}{q}_w^h={[{\left(\mathrm{\δ}{r}_w^h\right)}^T,{\left(\mathrm{\δ}{\mathrm{\Θ}}_w^h\right)}^T]}^T$ Degree of freedom for the targeting scheme physical constraints.

Advantage of the present invention is: (1) is applicable to the targeting scheme analysis and the design of various planform workpiece; (2) can verify the feasibility of the anchor clamps targeting scheme of having drafted; (3) can correctly revise existing anchor clamps scheme; (4) can reasonably confirm positioning reference, anchor point number and layout thereof; (5) theoretical foundation is provided for the exploitation of Computer Aided Fixture Design system.

Description of drawings

Fig. 1 is prismatic column workpiece of the present invention and finished surface instance graph;

Fig. 2 sets up first anchor point instance graph for the present invention at first positioning reference of prismatic column workpiece;

Fig. 3 sets up second anchor point instance graph for the present invention at first positioning reference of prismatic column workpiece;

Fig. 4 sets up the 3rd anchor point instance graph for the present invention at first positioning reference of prismatic column workpiece;

Fig. 5 sets up the 4th anchor point instance graph for the present invention at first positioning reference of prismatic column workpiece;

Fig. 6 resets the 4th anchor point instance graph for the present invention on second positioning reference of prismatic column workpiece;

Fig. 7 sets up the 5th anchor point instance graph for the present invention at second positioning reference of prismatic column workpiece;

Fig. 8 is not groove of the present invention " 4-2-1 " targeting scheme instance graph;

Fig. 9 is an instance graph before first locator scheme revision of not groove of the present invention;

Figure 10 is first locator scheme revision back instance graph of not groove of the present invention;

Figure 11 is an instance graph before second locator scheme revision of not groove of the present invention;

Figure 12 is second locator scheme revision of not groove of the present invention back instance graph;

Figure 13 is the 3rd locator scheme case figure of not groove of the present invention;

Figure 14 is not setting up anchor point 8 instance graphs on groove first positioning reference for the present invention;

Figure 15 is not reseting anchor point 8 instance graphs on groove second positioning reference for the present invention;

Embodiment

Through the concrete application of specific embodiment explanation pointwise algorithm for design in the targeting scheme design process, note ξ _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 ξ _γ=[0,0,0,0,0,1] ^TOne group of orthonormal basis of expression sextuple space.Respectively " generation " of the present invention formula pointwise algorithm for design and " revision " formula algorithm for design are done further to describe in detail below in conjunction with accompanying drawing and embodiment.

Embodiment 1:

Suppose that workpiece is the prismatic, as shown in Figure 1 of rule.Work surface is a ledge surface, requires to guarantee processing dimension a and b.For this reason, the most key link is exactly the appropriate design targeting scheme in the process, to confirm the tram and the direction of the relative cutter of workpiece.The design process of targeting scheme is following in detail:

Step 1: in order to guarantee processing dimension a, b on X and the Y direction simultaneously, theory constraint degree of freedom δ q _w=ξ λ, wherein base vector ξ=ξ _z, arbitrary number vector λ=λ _z, therefore k is arranged _Min=5;

Step 2: because the workpiece lower surface is the operation benchmark, so selection should the surface be first positioning reference, and first anchor point of layout, it is as shown in Figure 2,

Step 3: calculate Jacobi matrix J=[0 ,-1,0 ,-z ₁, 0, x ₁], therefore, rank (J)=1, so rank (J ξ)=0 is k '＜k _Min

Step 4: according to k '＜k _MinAnd rank (J)=k can know that targeting scheme belongs to owe positioning form, is unreasonable targeting scheme, and knows that the effective number of anchor point is not enough, thus should be on identical positioning reference second anchor point of layout, as shown in Figure 3,

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

Step 6: according to k '＜k _MinAnd rank (J)=k, can know targeting scheme still belong to owe the location, so the continuation on first positioning reference the 3rd anchor point of layout, as shown in Figure 4,

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

Step 8: the targeting scheme of this moment still belongs to owes the location, on first positioning reference, sets up the 4th anchor point for this reason, and promptly k=4 is as shown in Figure 5,

Step 9: the Jacobi matrix that continues the compute location scheme $J=\left[\begin{array}{cccccc}0& -1& 0& -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& -z_2& 0& x_2\\ 0& -1& 0& -z_3& 0& x_3\\ 0& -1& 0& -z_4& 0& x_4\end{array}\right],$ Know rank (J)=3 easily, so rank (J ξ)=1 is k '＜k for this reason _Min, rank (J)＜k;

Step 10: according to k '＜k _MinAnd rank (J)＜k can know, the targeting scheme of this moment was for owing the location, and knowledge anchor point number is not only not enough, and layout is also unreasonable.Therefore, need select left surface according to the datum coincidence principle be second location benchmark, and with the 4th anchor point layout on the new location benchmark of selecting, as shown in Figure 6;

Step 11: the Jacobi matrix of targeting scheme shown in the calculating chart $J=\left[\begin{array}{cccccc}0& -1& 0& -{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& -z_2& 0& x_2\\ 0& -1& 0& -z_3& 0& x_4\\ -1& 0& 0& 0& z_4& -y_4\end{array}\right],$ Therefore, rank (J)=4, so rank (J ξ)=0 is k '＜k _Min

Step 12: according to k '＜k _MinAnd rank (J)=k can know this targeting scheme for owing the location, and obviously the anchor point number is not enough, therefore on second positioning reference, continues the 5th anchor point of layout, and is as shown in Figure 7;

Step 13: the Jacobi matrix of calculating chart 9 targeting schemes does $J=\left[\begin{array}{cccccc}0& -1& 0& {-\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& {-z}_2& 0& x_2\\ 0& -1& 0& {-z}_3& 0& x_3\\ -1& 0& 0& 0& z_4& {-y}_4\\ -1& 0& 0& 0& z_5& {-y}_5\end{array}\right],$ Therefore rank (J)=5 is arranged, so rank (J ξ)=0 is k '=k _Min

Step 14: if according to k '=k _MinAnd rank (J)=k, and k＜6 can know that targeting scheme shown in Figure 9 for the part location, belongs to the correct positioning scheme.Therefore, this targeting scheme can be confirmed position and the direction of workpiece with respect to cutter, thereby can guarantee the requirement of machining precision;

Embodiment 2:

In order to obtain not design size a, b, the h requirement of groove, must at first reasonably confirm workpiece and cutter in the process

Between relative position.Intend for this reason and adopt " 4-2-1 " targeting scheme shown in Figure 8, and it is carried out labor revise with correct, its process is following:

Step 1: in order to obtain design size a, h, b on three directions simultaneously, theory constraint degree of freedom δ q _w=0, base vector ξ=0.Therefore k counts in minimum location _Min=6;

Step 2: can know in the targeting scheme location k=7 that counts by Figure 13, the easy for calculation Jacobi matrix gets $J=\left[\begin{array}{cccccc}0& -1& 0& {-\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="H2009101865544E000111.png,H2009101865544E00015.png"\; state="\{\{state\}\}">z</figure-callout>}}_1& 0& x_1\\ 0& -1& 0& {-z}_2& 0& x_2\\ 0& -1& 0& {-z}_3& 0& x_3\\ 0& -1& 0& {-z}_4& 0& x_4\\ -1& 0& 0& 0& z_5& {-y}_5\\ -1& 0& 0& 0& z_5& -y_6\\ 0& 0& -1& y_7& {-x}_7& 0\end{array}\right],$ Therefore rank (J)=5 is arranged, so rank (J ξ)=0 is k '=5;

Step 3: according to k '＜k _MinAnd rank (J)＜k can know that targeting scheme belongs to and owe the location, is unreasonable targeting scheme, and knows that the effective number of anchor point is not enough, and layout is also unreasonable;

Step 4: with the targeting scheme among Fig. 8, resolve into a plurality of locator schemes, at first select first positioning reference (being the workpiece lower surface) and form first locator scheme with the anchor point of layout on it according to the importance of positioning reference; Like Fig. 9, since k=4 in this moment locator scheme, rank (J)=3; So rank (J) (=3)＜k (=4); Therefore on first positioning reference, remove an anchor point, suppose and remove anchor point 4, shown in figure 10;

Step 5: because rank (J) (=3)=k (=3) in the targeting scheme shown in Figure 10; So the anchor point that continues to elect second positioning reference additional member and go up layout forms second locator scheme, and is shown in figure 11, through analyzing, calculate k=5; So rank (J)=4 is rank (J) (=4)＜k (=5).Therefore on second positioning reference, remove an anchor point, suppose and remove anchor point 6, shown in figure 12;

Step 6: because rank (J) (=4)=k (=4) in the targeting scheme shown in Figure 12 is shown in figure 13 so the anchor point that continues to elect the 3rd positioning reference additional member and go up layout forms the 3rd locator scheme, through analyzing, calculate rank (J) (=5)=k (=5);

Step 7: because the 3rd positioning reference is last positioning reference, thus on first positioning reference, set up first anchor point, the anchor point 8 among Figure 14, owing to effectively locate k '=5 of counting, k counts in minimum location _Min=6, and rank (J) (=5)＜k (=6).

Step 8: should anchor point 8 be reseted on second positioning reference, shown in figure 15, when anchor point 8 and anchor point 5 have identical Y to coordinate time, rank (J)=6, like this, effective k '=6 of counting, location, k owing to count in minimum location _Min=6, so k '=k _Min, so far, design process finishes.

Claims (1)

1. method through the correct positioning fixture of pointwise is characterized in that this method comprises two kinds of pointwise algorithm for designs:

First kind of pointwise algorithm for design comprises the following steps: that (1) analyze processing request, confirms the theory constraint degree of freedom and calculates minimum location and count; (2) select first positioning reference, then first anchor point of layout on selected positioning reference; (3) judge the correctness of current targeting scheme, if belong to full location, then targeting scheme is correct, and design process finishes; Owe the location if belong to, then the anchor point number is not enough, execution in step 4; If belong to and owed the location, then the anchor point number is not enough and layout is also unreasonable, execution in step 5; (4) the next anchor point of layout on identical positioning reference, execution in step 3; (5) the last anchor point of deletion is selected next positioning reference then, and on this positioning reference the next anchor point of layout, change step 3 afterwards over to;

Second kind of pointwise algorithm for design comprises the following steps: (1) analysis processing request, confirms theory constraint degree of freedom δ q _wAnd calculate minimum and locate the k that counts _Min, base vector ξ, actual location count k, effectively the order rank (J) and the rank (J ξ) of Jacobi matrix of k ', targeting scheme counts in the location; (2) correctness of the current targeting scheme of judgement, if targeting scheme is unique location or part location, targeting scheme is correct, then design process end; Owe the location if current targeting scheme belongs to, then execution in step 3; If current scheme belongs to and owed the location, then execution in step 6; Cross the location or partly cross the location if belong to unique, then execution in step 10; (3) select first positioning reference to analyze, and on this positioning reference plane, set up an anchor point, together with other anchor points on this reference field as a locator scheme independently; K ' counts in effective location of (4) calculating this locator scheme ₀, if k ' ₀=k _Min, then targeting scheme is correct, and design process finishes; If k ' ₀＜k _Min, then execution in step 5; (5) judge the relation of counting in the sum of ranks location of Jacobi matrix, if rank (J)=k, the next anchor point of layout on the newly-increased face of current locator scheme then, upgrading this scheme is the locator scheme, execution in step 4; If rank (J)＜k then deletes the up-to-date anchor point of setting up, increase next positioning reference, and on this positioning reference, set up an anchor point, together with the anchor point on this benchmark and the previous benchmark thereof, as the locator scheme of upgrading, execution in step 4; (6) select first positioning reference, with the anchor point on this benchmark as a locator scheme; (7) the count relation of k of order rank (J) and the location of judging Jacobi matrix in this locator scheme, if rank (J)＜k, then execution in step 8; If rank (J)=k, then execution in step 9; (8) on the positioning reference of current up-to-date interpolation, reduce by an anchor point, upgrading this scheme is the locator scheme, execution in step 7; (9) on current locator scheme basis, increase next positioning reference, upgrading this scheme is the locator scheme, judges whether this locator scheme is consistent with current targeting scheme, if consistent, then execution in step 3; If inconsistent, then execution in step 7; (10) select first positioning reference, with the anchor point on this benchmark as a locator scheme; (11) relation that in the analyzing and positioning subscheme count in the sum of ranks of Jacobi matrix location, if rank (J)＜k, then execution in step 12; If rank (J)=k, then execution in step 13; (12) anchor point of deletion on the positioning reference of current up-to-date interpolation, upgrading this scheme is the locator scheme, execution in step 11; K ' counts in effective location of (13) calculating this locator scheme ₀, if k ' ₀=k _Min, then targeting scheme is correct, and design process finishes; If k ' ₀＜k _Min, then execution in step 14; (14) on former locator scheme basis, increase next positioning reference, upgrading this scheme is the locator scheme, execution in step 11.

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