機(jī)械設(shè)計(jì)外文翻譯--自動(dòng)識(shí)別機(jī)械裝配中的幾何約束（英文）

1、Automatic identification of geometric constraints in mechanical assembliesS H Mullins? and D C Anderson?*Mechanical assemblies of manufactured components involve sets of relations between mating surfaces and functional c

2、haracteristics. Components must fit together to assemble and function properly, placing constraints on the allowable values of the component dimensions. Kinematic motion of the components is often necessary, resulting in

3、 other geometric constraints. Identification of constraints in models of mechanical assemblies is necessary for simulations of the effects of dimension and tolerance changes. This paper presents techniques for the automa

4、tic identification of such constraints in computer models of three-dimensional assemblies with nonorthogonal contacts between component surfaces and kinematic joints. The approach relies on a graph-based representation o

5、f the assembly. Search algorithms for identifying assembly constraints in this graph are presented. ? 1998 Elsevier Science Ltd. All rights reservedKeywords: assembly modeling, mechanical assemblies, con- straintsINTRODU

6、CTIONThe identification and solution of constraint relationships between component dimensions in mechanical assemblies is a significant problem in computer-aided design. Physical contacts between components create constr

7、aints on the relative position of the components, their nominal dimen- sions, and the tolerances on those dimensions. The number of such constraints can be large even for relatively simple assemblies. Specialized techniq

8、ues are needed to account for such geometric constraints. The constraints identified can be used to: (1) provide dimension sensitivity feedback to the designer; (2) identify relationships that the designer may not recogn

9、ize or fully comprehend; (3) allow for reduction of design time by making it easier to modify theexisting design; and (4) be useful for both top-down and bottom-up design modes. Top-down assembly design systems create fu

10、nctional constraints which the geometry must satisfy. Bottom-up assembly design uses the geometry to define constraints on the design’s behavior. Both approaches result in con- straints that arise from contacts and conne

11、ctions between the components of the assembly, and in either approach it is necessary to maintain the consistency of the assembly throughout design changes. Computer support for integrated design of parts and assemblies

12、requires constraint identification and management. There are two categories of geometric assembly relation- ships: mating conditions and kinematic joints. In general terms, a mating condition is a geometric relationship

13、between two or more components that has significance in the design or fabrication processes. Mating conditions include relationships which involve contact between parts, as well as relationships in which two parts do not

14、 have contact, such as clearance conditions. The distinction between mating conditions and kinematic joints is that the geometric relationship of a mating condition is static. A mating condition defines a relationship be

15、tween compo- nents that may not hold if changes occur in the dimensions of the components. In contrast, a kinematic joint is a geo- metric relationship between two components that allows relative motion and holds despite

16、 changes in the compo- nent’s dimensions. The kinematic joint is a functional spe- cification, but the mating condition is not. Examples of kinematic joints are the revolute joint and the prismatic joint. A mating surfac

17、e is a surface on a component that is involved in a mating condition. The mating surfaces of a component, or of a group of components connected by kine- matic joints, can restrict the range of values of the compo- nents’

18、 dimensions and the degrees of freedom (DOF) of the kinematic joints. A set of components that are related by a set of kinematic joints is a kinematic group, and a single component or a kinematic group is a constrained g

19、roup. The term constrained group infers there are geometric relation- ships between the mating surfaces that (1) are not identifiable as assembly constraints, and (2) are useful in identifying and formulating assembly co

20、nstraints. For a sin- gle component, these geometric relationships are the com- ponent’s dimensions and tolerances. For a kinematic group, they also include the DOF of the kinematic joints. An assembly constraint is crea

21、ted by mating conditionsComputer-Aided Design, Vol. 30, No. 9, pp. 715–726, 1998 ? 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0010-4485/98/$19.00+0.00 PII: S0010-4485(98)00026-8715*To whom co

22、rrespondence should be addressed. Tel: (765) 494-5720; Fax: (765) 494-0811; e-mail: dave@ecn.purdue.edu ?Structural Dynamic Research Corporation, Milford, OH 45150-2789, USA ?School of Mechanical Engineering, Purdue Univ

23、ersity, West Lafayette, IN 47906-1288, USA Paper Received: 5 April 1996. Revised: 10 March 1998. Accepted: 20 March 1998mating surfaces of component A can combine to restrict its motion in the two-dimensional subspace of

24、 E3 defined by the plane of the paper. No pair of mating surfaces can restrict the translation of the component in this subspace. Such a set of mating surfaces is defined as a physically constraining face set (PCFS). The

25、 PCFS is significant because without such a set of mating surfaces, the compo- nent dimensions in the constrained group could be changed without regard to the other components in the assembly. The constrained group coord

26、inate system could translate due to changes in the dimensions of any of the components in the assembly. The next section describes a general mathemati- cal definition of PCFS that will enable the identification of genera

27、l translational constraints on components.Characteristic vector spaceEach mating surface has a characteristic vector (CV) space of directions for which it prevents translation of the associated constrained group. Figure

28、4 demonstrates the CV spaces for several types of mating surfaces. In Figure 4a, the planar surface mating against another surface has a CV space defined by a? q and a ? 0 in which ? q has the same direction as the surfa

29、ce normal. The cylinder of Figure 4b in a cylindrical fits condition has a CV space also defined by a? q, a ? 0, where ? q is derived from? q ¼ c? qx þ d ? qy (2)c2 þ d2 ¼ 1 (3)? qx and ? qy are ortho

30、normal vectors perpendicular to the axis of the cylinder.The CV space for a spherical mating surface is defined similarly in Figure 4c. ? qx, ? qy and ? qz orthogonal vectors and the CV space is then given by a? q, a ? 0

31、, where? q ¼ c? qx þ d ? qy þ e? qz (4)c2 þ d2 þ e2 ¼ 1 (5)The CV space for a free-form parametric surface is defined by the surface normal and the surface parameters. The CV space is then d

32、efined by a? q, a ? 0, where? q ¼ ? q(s, t) þ??sr ? ??trk ??sr ? ??trk (6)in which r ¼ r(s, t) is the position of a point on the surface for the given parameter values.Algebraic identification of component

33、 spatial constraintsThese CV spaces can now be used to identify the PCFS for constrained groups. Two mating surfaces are required to restrict the constrained group’s translation in a one- dimensional subspace of E3. That

34、 is, the characteristic vector spaces for the pair of mating surfaces must both span, and be restricted to, a one-dimensional subspace. This requirement can be expressed asa1 ? q1 þ a2 ? q2 ¼ 0 (7)a1 ? 0 (8)a2

35、? 0 (9)If eqns (7)–(9) have a solution for the variables a1 and a2 then mating surfaces 1 and 2 form a one-dimensional con- straint. The important physical aspect of the relationship in eqn (7) is that, if the relationsh

36、ip does not hold, the mating surfaces are not mutually constraining. Any of the CV spaces can be inserted into the relationship of eqn (7) pro- vided the auxiliary constraints of eqn (3) or eqn (5) are included when appr

37、opriate. In the case of a one-dimensional constraint, eqns (7)–(9) have a solution only if ? q1 and ? q2 can be made to be equal and opposite. The generalization of eqns (7)–(9) to two- dimensional constraints can be der

38、ived by examining Figure 3. For the translation of the constrained group of part A to be completely restrained, it must not be possible to impose a displacement of ai ? 0 along any of the char- acteristic vectors ? qi wi

39、thout this resulting in a displacement of aj ? 0 along some other characteristic vector ? qj. This requirement can be summarized by the following relationshipsa1 ? q1 þ a2 ? q2 þ a3 ? q3 ¼ 0 (10)aj ? 0 (11

40、)a2 ? 0 (12)a3 ? 0 (13)Again, any of the characteristic vector spaces can be sub- stituted into eqn (10) with the stipulation that all auxiliary relations, such as those of eqn (3) and eqn (5), are included. The relation

41、ships between the characteristic vectors canGeometric constraints in mechanical assemblies: S H Mullins and D C Anderson717Figure 3 Two-dimensional physically constraining face set (PCFS)Figure 4 Characteristic vector sp