Representations and Methodologies for

Assembly Modeling

Kevin W. Lyons, Venkat N. Rajan and Raj Sreerangam

1.0 INTRODUCTION

Most manufactured products are assemblies of components. The number of components

can range from a few tens in small assemblies to a few millions in large assemblies such as

aircraft. The design and manufacture of these assemblies i s a daunting task, especially

under limited time-to-market constraints.

Design of electro -mechanical products involves the description of the relationships

between a group of parts that allows them to behave in the desired fashion. T h i s includes

the description of relative motion between components, fit requirements, and joint

strength requirements. The assembly modeling activity parallels the top-down design pro-

cess [Ulrich and Eppinger, 19951. During the conceptual design stage, the designer(s) may

be evaluating the kinematic capabilities of a particular design. At this stage, the types of

kinematic joints constituting the concept wil l be known, however, most of the geometry

remains to be specified. During the preliminary design stage, after a particular concept has

been selected for further exploration, the geometric layout information i s specified. The

layout specifies the type of architecture (modular or integral), and the relative position and

orientation of major chunks (or subassemblies) within the product by taking into account

Representations and Methodologies for Assembly ModelingJanuary 2,1997 1

the functional interactions between the chunks. During the detailed design phase, these

chunks are further decomposed to create the geometry of smaller subassemblies and com-

ponents, until a sufficiently unambiguous manufacturing process description i s created. I t

i s clear that assembly related issues are an important part of the product design and manu-

facturing activities. As indicated by Whitney [1996] assembly may form the basis for inte-

grating al l the product realization and life-cycle activities.

During the design process, various types of analyses are conducted on the design to ensure

that the product meets the functional requirements, i s easy to manufacture and assemble,

and meets other criteria such as maintainability, recyclability, etc. Incidental interactions

caused by the geometric layout are also evaluated to identify redesign needs. Th i s leads to

an iterative process of design and analysis.

Many tools have been created to support various stages of the design process. Some proto-

type systems, such as the Conceptual Assembly Modeling Framework (CAMF) [Kim et

al., 19963, have been created to support the conceptual design process, with particular

focus on the assembly modeling activity. Other approaches to conceptual design have pri-

marily focussed on capturing the design intent. These systems do not capture the assembly

joint information that i s generated during the concept design. Certain mechanical design

software systems, such as A D A M S M S , allow the designer to model and analyze the kine-

matics of the mechanism. Commercial CAD systems allow the designer to specify the

geometry of individual components and are thus useful only during the detailed design

stage. Recently, these systems have provided some basic assembly modeling capability.

T h i s includes a specification of the hierarchical assembly structure, and mating constraints

between components. Other kinematic modeling and analysis tools such as ROBCAD or

Representations andMethodologies for Assembly ModelingJanuary 2. 1997 2

IGRIP may need to be used to verify the kinematic behavior of the fully designed product.

Thus, the designer may use a variety of tools during the design process to ensure that a sat-

isfactory design i s created. He/she may start with a conceptual design tool to specify the

design rationale for a particular concept, use a kinematic modeling and analysis tool to

perform preliminary kinematic design and analysis of the concepts, use a CAD tool to per-

form detailed design of the components and respecify the joint information in the form of

mating constraints, and finally import the geometry into a kinematic modeling and analy-

sis tool, respecify the joint information, and evaluate the motion characteristics with the

fully specified geometric model of the product.

One major deficiency that i s evident from the above description i s the repeated specifica -

tion of the same joint information during the conceptual, preliminary, and detailed design

phases. T h i s raises the question of whether it i s possible to specify the joint information

during the conceptual design stage and propagate/verify it during the preliminary and

detailed design stages. T h i s implies that

1. Representation schemes need to be identified that wil l facilitate the capture of joint

information during the various stages of design, and

2. Methodologies need to be developed to propagate/verify this infohation during the

preliminary and detailed design stages by comparing the information generated during

these stages against the joint information specified in the conceptual stage.

The representations will also be important for exchange of information between modeling,

analysis, and planning systems. CAD vendors have developed many different ways to rep-

resent mating constraints. I t i s not clear that all of these representations are capturing the

Representations and Methodologies for Assembly ModelingJanuary 2, 1997 3

same information. While the issue of exchanging mating information between modeling

systems i s critical for unrestricted exchange of product data, litt le has been done in terms

of developing standard representations that specify the type of mating constraints that

needs to be captured during the various design stages. STEP has some limited assembly

design representations that capture the assembly structure and the kinematic joint informa -

tion during the conceptual design process. However, these representations may not be

complete and may not be useful in the preliminary and detailed design stages.

In the following sections, we specify the type of information generated during the various

stages of design and propose representations that willbe suitable for capture of th i s infor-

mation. We also provide some basic methodologies to verify that the surface mating con-

straints specified during the preliminary and detailed design stages are consistent with the

kinematic joint information specified during the conceptual design stage, and to propagate

these constraints down the assembly structure during the detailed design stage. The useful-

ness of the proposed representations for assembly analysis and planning activities, and

their impact on the development of the STEP standard are also discussed. Lastly, a

description is provided of the prototype Assembly Modeling System implementation that

has been developed to test the proposed representations and methodologies.

2.0 ASSEMBLY DESIGN INFORMATION

Various types of assembly information are generated during the different stages of design.

During the conceptual design stage, kinematic joints are defined. During the geometric

detailed design stage, these kinematic joints are realized by means of surface mating con-

Representations and Methodologies for Assembly ModelingJanuary 2, 1997 4

straints. During the top-down decomposition of the subassemblies in this stage, the sur-

face mating constraints are further refined to relationships between lower-level

subassemblies and finally, components. In the following sections, we will discuss the type

of information generated during these various stages. T h i s wi l l provide a basis for identi-

fying the types of joint representations that are suitable for the various stages of design.

We will also present methodologies to automatically infer joint kinematics based on sur-

face mating constraints, and to automatically propagate these constraints during the top-

down decomposition process.

2.1 Conceptual Joint Design

A functional specification of a product specifies how material, energy, and signals are

transformed to accomplish a certain set of requirements. T h i s transformation i s accom-

plished by various means including mechanical, electrical, thermal, and fluid interactions.

For example, in an internal combustion engine, fuel and air need to be delivered to the

combustion chamber, chemical energy needs to be transformed into mechanical energy,

and the mechanical energy needs to be supplied to some external elements. Mechanical

interactions typically involve motions of certain subassemblies relative to others within

the product. The concept is realized by the way in which this mechanical motion i s accom-

plished. Thus, in a piston engine, the motion of the piston relative to the cylinder i s a

mechanical interaction. Thermal and fluid interactions may induce or be induced by

mechanical interactions in certain cases. For example, the compression of the fuel-air mix -

ture in the combustion chamber as well as the expansion of the combustion gas products i s

accomplished by the motion of the piston relative to the cylinder. Thus, the fluid interac -

Representations andMethodologies for Assembly ModclingJanuary 2 1997 5

tions are accomplished by mechanical means. In other cases, such as the delivery of fuel to

the valves or dissipation of the exhaust gases beyond the valves, no mechanical motion i s

involved.

While al l these interactions need to be considered in order to capture the characteristics of

the joints within the product, in this paper, we wil l focus only on the mechanical interac -

tions. In the following sections, we will review the related literature in conceptual design,

review Part 105 of STEP that contains kinematic representations, and propose a represen -

tation of mechanical products that i s suitable to capture the information about mechanical

interactions.

2.1.1 Conceptual Assembly Design Literature Review

Various attempts have been made to provide tools to designers during the conceptual

design stage. Some have focussed on purely capturing the design intent, while others have

attempted to actively support the design process by generating designs for special problem

classes. The Conceptual Assembly Modeling Framework (CAMF) developed by Kim et

al. [1996] i s an example of the first approach in which a system i s developed to capture the

design intent. The system has a total of 11 stages, starting from the specification of cus-

tomer requirements and development of product specifications, to perfonning detailed

design. The system allows the designer to explore alternatives in a structured manner.

Approaches to generative design have focussed on the use of bond graphs to model inter-

actions and generate feasible designs [Ulrich and Seering, 1990, Rinderle and Balasubra -

maniam, 19901. Ulrich and Seering [1990] describe a methodology to increase function

sharing in a mechanism design. The approach used involves deleting an element from the

Representations and Methodologies for Assembly ModelingJanuary 2. 1997 6

physical representation, identifying alternate features in the remaining design that can

potentially implement the functions supported by the deleted element, and modifying the

secondary properties of these features to accomplish the implementation. Explicit repre-

sentations of functional specifications or the physical product model are not used in this

procedure. Welch and Dixon [1991] extend the bond graph representation to explicitly

represent position and orientation information, and use vectors to represent efforts and

flows. They also consider various types of flows (thermal, fluid, etc.) as well as systems

that have multiple inputs and outputs.

Extensive research has been performed with particular emphasis on assembly modeling.

T h e CAMF framework [Kim et al., 19961 evolved from the need to integrate assembly

design and planning. Libirdi et al. [19881 discuss the requirements of a conceptual design

environment for Mechanical Systems and Assemblies (MSAs). They indicate the need to

support the top-down design process, methods to allows designers to work at abstract con-

ceptual levels with abstract geometry, and multiple functional viewpoints (structural, kine-

matic, electrical, etc.). Mantyla [1990] and Gui and Mantyla [1994]describe the WAYT

and DELTA systems that support modeling of mechanical assemblies. The WAYT system

provides multiple views of the product organized using hierarchical part-of graphs. A

design browser allows the user to edit these graphs, while a geometry browser i s used to

create and edit the geometric model. A constraint browser i s also provided to allow the

designer to specify constraints that are then solved using an incremental constraint satis-

faction algorithm. The DELTA system presents a more complete description of the assem-

bly model by considering two different views of the product: function -oriented and

module-oriented. The top-down decomposition of the product i s viewed as a recursive

Representations andMethodologies for Assembly ModelingJanuary 2. 1997 7

subdivision into function carriers which are mapped into components or connectors.

Components perform desired functions while connectors provide constraints between

components.

Liu and Fischer [1993] present an assembly application protocol in which assemblies are

represented as parts and joints. Joints can be of three types: operational, fastener, and

fusion. Operational joints have integral fastening elements such as snaps, clips, etc., fas-

tener joints require additional fastening elements, and the fusion joints require fusion

operations, presumably representing welded joints. They show how the protocol i s related

to the STEP part definition standards.

Cutkosky et a1.[1992] describe a concunent design system that supports various stages of

the design process. At the highest level, an assembly i s represented as a graph consisting

of components and their interactions. These interactions impose certain constraints on the

mating relationships between the components. At the next level of definition, components

have ports that define standard connectivity relationships. Standard components such as

bolts, and nuts have pre-defined ports, but the user can define ports on new components.

Ports are further decomposed into component features such as holes and protrusions,

which are further decomposed into lower-level geometric information. The approach used

i s to derive lower -level geometric and kinematic information based on higher level con-

nection definitions. It i s indicated that the process of identlfying higher level joint defini-

tions given the lower level information is simi lar to the feature recognition problem in

process planning.

Joskowicz [1990] describes a methodology to identlfy kinematic mechanisms that are

Representations andMethodologies for Assembly ModelingJanuary 2,1997 a

equivalent in their behavior. The purpose of determining equivalence classes i s to allow

designers to efficiently retrieve mechanisms for use during design activities. Local behav-

ior of pairs of objects are f i r s t determined and used to compute the global behavior of the

entire mechanism. Local behaviors are computed based on the degrees of freedom of the

components and their mating geometry, while the global behavior i s computed by com-

posing the local behaviors using symbolic rules and a constraint propagation algorithm.

Henson et al. (19931 describe a functional representation of the assembly model that

relates the functional specifications with the physical structure of the product. A tree - like

structure i s created in which the top level nodes represent functions while the children

nodes represent the assembly components.

Whitney [19961 defines two types of assemblies: small and large. Assembly in the small i s

used to refer to individual part matings while assembly in the large refers to the product

architecture and related issues such as tolerance propagation, planning, etc. The informa-

tion included in a data model for assembly in the small i s part geometry and mating fea-

tures, tolerances, assembly process time and cost, tooling, etc. The corresponding

information for assembly in the large includes mating sets for each part, where-used infor-

mation, tooling points, vendor information. etc. H e also discusses the use of nominal

assembly models in assembly planning and varied models in tolerance propagation.

El Dahshan and Barthes [1991] describe an assembly representation that uses part-of rela-

tions. A constraint propagation approach i s described in which a change in a constraint is

propagated from the component level to the assembly level using the part-of relationship

and then propagated down to other components from the assembly level. The constraint

Rcprsentations andMethodologies for Asscmbiy McdcliigJanuq 2,1997 9

satisfaction approach checks ifall global constraints have been satisfied at the assembly

level before accepting the change. Otherwise i t declares failure and resets the constraint

values.

Pratt [1996] proposes a constraint schema for STEP. Constraints are divided into two cate-

gories: dimensional and logical. These constraints are expected to cover the needs of con-

straint based modeling in the design of parts and assemblies. Dimensional constraints

include distance, angle, and radius value relationships. Geometric constraints include on,

parallel, parallel -offset, perpendicular, symmetric, tangent, midpoint, equal-length, equal -

radius, coincident -location, point-at-intersection, direction, and fixed relationships.

Sugimura et al. E19941 describe an assembly model under the STEP framework. T h i s

model contains information about individual parts, standard parts, a hierarchical represen -

tation of structure, position and orientation of parts, tolerances, connecting relationships

between components, and assembly form features. Three types of component relations are

specified: connecting, intermittent -connecting, and non-connecting. A connecting rela-

tion is further decomposed into movable and fixed connections. The movable connection

i s related to the kinematics model presented in STEP Part 105, and uses the standard joint

definitions described there. Other elements of the assembly model such as features, and

assembly structure are related to the appropriate representations included in STEP Parts

41,43,44, and 48. They present one of the most comprehensive treatments of a standard

assembly representation. However, many elements within the representation are not fully

defined. I t i s clear that an assembly model should contain the joint information that pro-

vides information on i ts kinematics as well as the surface mating relationships that realize

the joints behavior. While the former i s related to the definitions given inPart 105, the lat:

Representations andMethodologies for Asscmbly ModclingJanuary 2, 1997 10

ter i s represented, with little accompanying detail, using assembly features that are charac -

terized as subtypes of the feature entity from Part 48. However, the characterization of

connecting relationships as connecting, intermittent -connecting, and non-connecting are

useful to capture a wide range of assembly component interactions.

2.1.2 Review of STEP Part 105

Part 105 of STEP [ I S 0 TC 184/SC4/WG3N265, 19931 provides a representation for

mechanical products that can be used during the conceptual design stage. We wil l briefly

review this representation below.

The kinematic model of a product consists of a ground representation and representations

for various mechanisms within the product. The ground representation specifies the global

coordinate system as well as a shape,representation for the immobile elements of the prod-

uct. Clearly, during the conceptual design stage, such shape information may not be avail-

able.

Each mechanism is defined by means of its topological structure, lower level link and joint

information, and the initial state defined by the vector of initial values of the joint vari-

ables. The topological structure i s represented by means of a graph G= (V,E), where the

vertex set V represents the links,and the edge set E represents the joints in the mechanism.

Th i s structure may consist o f network (for open kinematic chains) and tree (for closed

kinematic chains) subgraphs. The network type subgraph i s represented by means of kine -

matic loops that represent a simply closed kinematic chain. Each loop i s specified by

means of relationships between joints. The orientation of each joint i s specified by its

advent link and the exi t link.For a tree subgraph, only the joint orientation i s required.

Representations and Methodologies for Asscmbly ModelingJanuary 2. 1997 11

The joint definition at the lower level consists of a description of the kinematic pair that

specifies the restriction between the motion of the two links attached to the joint. The

kinematic pair specifies the joint type, joint variables, and the allowable range of motion

for the various joint variables. Twelve different kinematic pairs have been proposed in

Part 105. They are:

1. Revolute pair: In such a joint, motion i s restricted to rotation of one link with respect

to the other about a given axis. The joint variable i s the angle of rotation between the

two reference frames about the z-axis, and the joint range i s specified by the lower and

upper l i m i t s of the angle of rotation.

2. Prismatic pair: In this case the motion between the links i s limited to a translation

along the common axis. The joint variable i s the distance of translation along the z-

axis, and the range of motion is given by the lower and upper limits on the translation.

3. Screw pair: T h i s pair requires simultaneous and coordinated rotational and transla -

tional motions about a common axis. The joint variables are the distance of translation

and the angle of rotation about the z-axis. However, the two variables are dependent

on each other by means of the pitch distance. The pitch specifies the linear translation

caused by one full rotation (i.e., 360 degrees). Thus, the range of motion i s only speci -

fied for the rotation, as the limits of the angle of rotation.

4. Cylindricalpair: In th i s joint, independent translation and rotation i s possible between

the two links about a common axis. The joint parameters are the angle of rotation and

the distance of translation about the z-axis. The joint l im i t s are specified as the upper

and lower limits of rotation and translation.

Reprcstntations andMethodologics for Assembly ModclingJanuary 2, 1997 12

5. Spherical pair: The motion between the links i s restricted to rotation about a common

point. The joint parameters are three angles of rotation specified about orthogonal

axes. The joint l imits specify the lower and upper limit o f rotation for each of the three

angle variables.

6. Planar pair: In a planar pair, contact needs to be maintained between planar faces of

the two links. Thus, translation i s possible in the x- and y-axis, and rotation i s possible

about the z-axis. The joint variables are the translation distances along the x- and y-

axes, and rotation angle about the z-axis. Lower and upper l im i ts are specified for the

two translations and the rotation.

7. Suq$ace pair: In this type of joint, motion occurs along surfaces on each of the links

such that at least a point contact i s maintained. The point of contact i s the same in the

global coordinate system whether approached from one surface or the other, with the

x-axes either aligned or opposing. The joint variables are the reference points on the

two surfaces and the orientation at the point of contact. The joint range is specified by

the extent of the surfaces on each of the links, and the limits on the angle of rotation

used to specify the orientation.

7.1. Sliding sugace pair A subtype of the surface pair, in which sliding occurs

between the two surfaces.

7.2. Rolling surface pair: A subtype of the surface pair in which a rolling contact i s

maintained between the two surfaces.

8. Curve pair: In this type of joint, motion occurs along a curve on each of the two l inks

such that a point of contact i s maintained. Both curves l ie in the same plane and the z-

Representations and Methodologies for Assembly ModelingJanuary 2.1997 13

axes are perpendicular to this plane. The y-z plane i s the common plane on which the

point of contact lies. The joint variables are the points on the two curves. The joint

l imi ts are defined by the extent of the curves on each o f the two links.

8.1. Sliding curve pair: A subtype of the curve pair, th is type of joint specifies sliding

motion along the curves.

8.2. Rolling curve pair: A subtype of -curve pair, this specifies a rolling contact

between the two curves.

9. Gear pair: Such a joint can be considered a special case of the rolling curve pair

(although, some sliding may also take place). In th is case, the second link has a rolling

motion along the first link.The motion of the f i rst link can be computed as the rotation

of the contact point about i ts z-axis. The motion of the second link can be computed

based on the motion of the f i rst link and the gear ratio. The upper and lower l im i ts on

the rotation of the f i rs t link spec@ the joint range.

10. Rack andpinion pair: T h i s i s also a special case of the rolling curve pair in which the

pinion and the rack l i e in the same plane. Rack is treated as the first link and the pinion

i s treated as the second link. Joint motion i s defined by the translation along the y-axis

of the f irst link. The rotational motion of the second link can be computed using the

pinion radius. Joint range i s defined by the upper and lower l im i ts on the distance of

translation along the first link.

Each mechanism in the product i s fully defined when the geometric shape information

related to a l l the joints and links is provided.

Representations and Methodologies for Asscmbly ModelingJanuary 2.1997 14

2.1.3 Proposed Conceptual Design Representation

During the conceptual design stage, the designer may only create a skeletal structure of

the product and i ts constituent mechanisms. The geometry information i s mostly unde-

fined. Therefore, at th is stage, the topological structure provides the best representation of

the product. Attributes attached to the nodes can be used to define some basic link infor-

mation such aslink lengths and reference coordinate frames. The edges of the graph struc-

ture represent joints. Various attributes need to be attached to each of the edges. The

primary attribute specifies the general joint type as being rigid or movable. Rigid joints

completely restrict the motion between the two links. I t i s important to provide the

designer the capability to define such joints without requiring details on how such joints

wil l be realized. Movable joints can be represented using the kinematic pairs defined

above. For such joints, the kinematic pair type (revolute, prismatic, screw, cylindrical,

spherical, planar, gear, rack-and-pinion, sliding -surface, rolling-surface, sliding-curve,

rolling-curve), and the joint variable range values need to be specified. The overall struc -

ture of this representation i s shown in Figure 1.

T h i s representation is similar to that specified in Part 105 of STEP. The major differences

are:

1. The geometry definition in Part 105 references the geometry and shape representations

from Parts 41 and 43. These representations are very detailed and wil l not generally be

populated to the fullextent during the conceptual design stage. In the proposed repre-

sentation, some basic geometry information related to the skeletal structure o f the

product i s being captured. This would reduce the size of the STEP file generated and

Representations andMethodologics for Assembly ModelingJanuary 2, 1997 1s

Type