MODELING METHOD FOR PRODUCT STRUCTURE MAPPING BASED ON REVERSE SOLVING OF LOCUS AND MOTION

1、modeling method for product structure mapping based on reverse solving of locus and motion*abstract: aiming at the problem of structure design in reverse -design of mechanism, a structure mapping method based on reverse solving of locus and motion (rs!.m) is presented. the mechanism scheme meeting t

2、he requirements of geometric anil structural feacurt; is obtained through rslm. the element instance subsets related to component arc estsbluhcu based on the element type mapping, pair structure type mapping ar,d desitw kncw!?dg* capping between components and elements layer by layer. the wembly pos

3、ition mapp:nc of elements is established based on the topological structure information of mechanis.71 s.,h!r,c, and the product modeling of structure mapping is realized. the algorithm /mogiam aid prototype system of product structure mapping based on rslm are developed. application samples show th

4、at the method implements the integration of scheme design, assembly design and structure design, and modeling for product structure mapping based on rslm. the feasibility of assembly is analyzed in scheme design that contributes to reducing the design error, and raising the design efficiency and qua

5、lity. key words: reverse solving mapping mechanism assembly modeling0 introductionin mechanism design, there are generally four phases: scheme planning, principle design, assembly modeling and part modeling. these phases constitute an interactive design process full of influences and constraints. ho

6、w to implement the design process modeling is important for improving the design efficiency and product quality121.gero3 made layered abstraction of the design information in terms of function, behavior and structure. he pointed out that the product forming process consisted of three stages: product

7、 function modeling, product behavior process and product structure modeling. kota, et al45, studied the methods for identifying the structure form function, and built up a function-structure model mapped from function to structure. qian, et al61, put forward the behavior concept based on analogy des

8、ign and presented a function-behavior-structure design model. chiou, et al71, devised a matrix representation scheme that not only captured the essential nature of the building blocks, but also enabled automatic decomposition of a given task into simpler sub-tasks. the essence of the decomposing pro

9、cess was combination design for framework from the top down, while the limitation was the lack of expressing the speed specialty of the motion. gorti, et al8., represented the mapping of function symbol and figure character from the viewpoint of integration of concept design and structure design. mi

10、chal, et al(9), defined the combination of figure symbol and function semanteme as function character. gui, et al 0), brought forward a product definition element which could describe the product information and had special engineering meanings and could exist in every layer of the product model in

11、order to implement the uniform expression of the product information. harmer, et al1, studied the modeling technology for products based on general components by identifying function requirement constraints and transforming them into appropriate property character and modeling with the proper compon

12、ents among the database by matching and comparison.the above methods studied the design process modeling in various aspects and developed the product design methodology. because the expression of product function, behavior and structure is more complex than geometry expression, it is difficult to im

13、plement the mappings between requirement, assembly and structure. in conclusion, the difficulty results from the absence of an integration method from mechanism scheme solution to assembly modeling then to part modeling. to overcome the difficulty, a modeling method for product design based on multi

14、layer mapping is presented in the paper. the mechanism scheme design is implemented through reverse solving of locus and motion (rslm). the assembly position mappings of the components are established on the basis of element type mapping, pair structure type mapping, and design knowledge mapping bet

15、ween components and elements layer-by-layer. the structure mapping modeling is implemented based on rslm.1 reverse solving of locus and motion1.1 reverse solving of locusin reverse solving of mechanism locus, the types and scales of mechanisms meeting the expected motion track requirements are ident

16、ified through curve similarity matching according to the expected motion track. the mechanism scheme subset m, meeting the expected motion track requirements is identified based on the reverse solving of locus.the locus curve is hypothetically put into an even-meshed grid. a moving point is used to

17、identify the grid direction and approximate the original locus curve farthest from the start point to the end point. the chain code sequence of the locus curve is produced. to eliminate the uncertainty in reverse solving of mechanism locus resulting from the inconsistent expressing standards, the lo

18、cus curve is expressed with chain code sequence uniformly through the chain code normalization.the normalization of the curve locus chain code is shown as fig. 1. apparently, there are four possible directions for the moving point at the intersection point of the grid: positive direction along x, ne

19、gative direction along x, positive direction along y, negative direction along y. the code unit in above four directions for one step is uniformly expressed as px, mx, py and my, respectively. for example, the chain codes of the locus curve are shown in fig. 1: px, my, px, px, px, my, px, my, px, my

20、, my, mx, my, mx, my, mx, mx, my and mx.therefore, the chain code can express the direction and fiture information of the original locus curve the expression precisicn depends on the density of the grid ths dose: the grid is the more accurate the expression is. or. the other hand, the normalization

21、of the chain code of the iocjk curve satisfies the requirements of translation invariability. at the same time, if the chain code is put into different grids with diverse densities to express the original curve, the locus curve can be scaled proportionally. furthermore, the reverse solving of mechan

22、ism locus is implemented based on the graph similarity of the locus curve quantized through geometric transformation and matching analysis of the locus curve chain code.1.2 reverse solving of motionthe requirements in mechanism design are not only the motion track but also the dynamic character in l

23、ocus curve, for example, the quick-return character in actuating mechanism. therefore, the mechanism scheme subset mk, which meets the dynamic character requirements can be obtained through velocity matching on the basis of subset mt, mtcm,. c is the locus of the moving point y(a,p) with the driving

24、 force shown in fig. 2. let x be the position of the driving mechanism, ya,p) can be expressed as ya,p) = f(x). x can be expressed with t, x = ht), so y(a,p) = fh(t) is gained. therefore, the velocity and acceleration of the mechanism in locus curve c can be respectively expressed as followsas shown

25、 in fig. 3, normal vector length of moving pointya,p) in locus curve is the velocity of the point.velocity curvev corresponding to the locus curve c can be obtained with eq.(2). generally speaking, among the t.echanism scheme subclassm, meeting the expected motion track requirements, the mechanism r

26、.chemesubclass m further meeting the expected dynamicalrequirements in locus curve can be classified into two differentilasjgn ia*i:s: onepoint velocity matching problem which requires vht relevant velocity relationship when the special isolate? points in locus curve are passed; the other is continu

27、ous velocity matching problem which requires velocity changing relationship when the matching mechanism passes the whole locus curve.(1) for exact point velocity matching problem, the velocity of one certain point y in locus curve is v = x v0 (v0 is the velocity of the drive mechanism). the necessar

28、y and sufficient condition is the velocity curve v passing through the point v, namely v e v . therefore, for 5 exact points velocity matching problem, the matching condition is: v, v2, , v, e v .(2) for continuous velocity matching problem, it is generally difficult to solve the mechanism scheme of

29、 continuous velocity changing in exact matching locus curve in engineering design. curve resemble matching algorithm is currently used, then the actual velocity curve v is selected to meet engineering requirements which farthest approximates the mechanism scheme of object velocity curve v0.on the ot

30、her hand, if the dynamic character of mechanism along locus curve is described with acceleration parameter, the acceleration curve a corresponding to locus curve c will be gained. similarly, the mechanism scheme meeting the special acceleration requirements in locus curve can also be selected in mec

31、hanism scheme subclass m, which satisfies the expected motion track requirements.2 methods for element structure layer mapping2.1 definition of elementin mechanism design, element is defined as parts or parts groups which implement the mechanism function together with the corresponding components in

32、 mechanism scheme. as shown in fig. 4, a pair of rail is composed of two elements: slide block and guide way, which are respectively corresponding to the two components constituting the translation pair in mechanism scheme.2.2 type mapping of components and elementscomponents in linkage can be class

33、ified according to the numbers and types of the pairs. to establish parameterization element database, some symbols are defined. u,(jlj2-jj are the homogeneous components which have n pairs: jj2,-,j. similarly, elements can also be classified according to the numbers and types of the pairs. c(jij2-j

34、ii) are the homogeneouselements which have n pairs: j,j2,-,j. in parameterizationelement database, the relative position pair size relevance mapping of the components and elements are implemented according to the parameterization rules about the homogeneous elements pair relative position relationsh

35、ips. as shown in fig. 5, fig. sa is parameterization rule definition of crrr) class. the uniqueness of the initiative size s, s2, s3 identifies the relative position size relationship of the pair in the type of element. fig. sb is parameterization rule driving transformation of cj(rrr) class element

36、.the components are mapped to their responding element database subclass in order to form the correct mapping relationships between components and elements. the correct mapping rules for implementing type mapping between components and elements are as follows.(1) mapping class component ult(jij2-jlt

37、)to element instance class c(y,y2-y,).(2) element parameterization rule driving transformation is implemented by class component u(j,j2-jj pair relativeposition size driving c(jij2-jj element parameterization rule.2.3 mapping of pair structure typein conceptual design of mechanisms, especially in de

38、tailed design process, the homogeneous pair j generally maps into various different structure types for election denoted as: 7(1), j(2), j(3),., shown in fig. 6.in part structure design, the pair structure type j(n) is identified through corresponding mapping rules according to the expected function

39、, working condition, selected part material, machining condition, etc. taking translation pair for example, the relevant components should be hydraulic jar and other sets of linear dynamic components when it is active pair. it should be selected from the structure type of rub pair when it is not act

40、ive pair while working condition is low speed and light load. it should be selected from the structure type of roll pair when it is not active pair while working condition is high speed and heavy load. in element database, n dimension vector is pair structure type r(r r2 ) f eacn element instance in

41、 the element subset c(jj2-jn), where variable rt i = 1,2,- ,/) is the pair structure type j, . consequently, the pair structure type of all element instpr.pcs of class instance cii(j,j2-jii) can be expressed uniformly with a matrix as follows where k is the number of component instance in class inst

42、ance. therefore, if rrr-r) is pair structure type of one component un(jxj2-j) in class instance which is mapped to component database cn(jij2-j) me correct pair structure type mapping relationship can be expressed as follows where rx is the x row vector in matrix j?*,.2.4 mapping of design knowledge

43、the component structure requirements are brought forward in perspective of implementing mechanism motion function in both component type mapping and pair structure type, each component in mechanism scheme is mapped to a pair of element instances which can implement the motion function.however, in st

44、ructure design of mechanism product, not only dynamical requirements of mechanism scheme should be satisfied but also the product functions and performance requirements in some special areas should be implemented.on the other hand, for some special mechanism products, the component structure commonl

45、y has series and comparability character because of the specialty of the product function. fig. 7 is the mapping modeling sketch of open and shut switch mechanism of a low voltage circuit breaker. the accepted element structure evidently has series and comparability character according to the concre

46、te product type of the design task (for example, plastic case type or framework type, etc), employing condition (for example, voltage or current, etc) and performance requirements (for example, subsection time or subsection velocity, etc). therefore, for some special areas, the corresponding mapping

47、 rules can be firstly set up. on the basis of the concrete product model and requirements for function and performance in design task process, each component in mechanism scheme is then mapped to a pair of element instance which can implement special design requirements precisely.3 topology driving

48、mapping of assembly position3.1 topology structure of linkagetopology structure of linkage expresses topology information about connecting relationship between each constituting component and every pair. on the basis of the linkage sketch, component is denoted with peak, pair is denoted with border,

49、 position coordinate of the pair is denoted with the power coefficient of the border, so topology structure of linkage can be made abstraction as a non-directed graph shown in fig. 8.where, frame is framework; b is the component whose subscript is / in framework scheme;,/ (x) is the pair whose subsc

50、ript is j, the pair type is x(x = rorp-).3.2 topology driving mapping of assembly positionin product assembly modeling driven by topology, each element is driven to the correct assembly position till reaching the certain assembly position in three assembly dimensions room through both the component

51、connecting relationship and the pair position information which are reflected in topology chart. this can be used for assembly navigation for improving the product assembly efficiency.product assembly modeling process is as follows. the topology structure graph is traversed in extent priority sequen

52、ce beginning from the peak frame. when the peak b ln the topologystructure chart is visited, element instance model c which is mapped from b, is read according to the value of b after being read, c ls loaded in assembly room. thus, the degree of peak b. denoted by td(bt) is the number of pair in ele

53、ment instance model c, therewith, all the borders which are associated with the peak g( are traversed. when the border (b ,b) is visited, pair j (x) is identified in element instance model c, which is corresponding with (fl,5) through the value of (bt,b) then, the power coefficient (x ,y) of the bor

54、der (fl,fl) is the position coordinate of the projection of the pairx)in x-y plane. the correct assembly position of the elements in x-y projection plane is then quickly established and constrained. if the orientation of each element in z axis is driven by some extra geometry constraints, the comple

55、xity during loading the geometry assembly constraints will be simplified. assembly position navi- gation algorithm driven by topology is expressed in fig. 9.4 application instanceon the platform of visual c+ and pro/engineer as well as pro/toolkit, a prototype system for the mechanism product design

56、 modeling has been developed based on multilayer mapping. the system is composed of three major modules: reverse solving of mechanism scheme, element mapping modeling and assembly position navigation. fig. 10 shows the design instance of grab bucket with two cheeks. fig. 10a shows the application instance in rever