Application of Screw Theory to Constraint Analysis of Mechanical Assemblies Joined by Features

Adams, Jeffrey; Whitney, Daniel E.

doi:10.1115/1.1334858

Cited by 53 publications

(28 citation statements)

References 18 publications

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“…Therefore, joints must be selected in such a way that no DOF is constrained twice not only among joints but also with locators. In such cases, the intersection of the wrench matrix corresponding to any subset of and the wrench matrix of any other disjoint subset must result in the zero matrix (14) which is also equivalent to (15) Further, in order to have all six DOFs constrained, (16) When any set of joint types and fixture elements satisfies (15) with the total rank less than six, it is considered to be feasible, assuming that additional fixtures or locators on existing fixtures will be arranged. Six less the number of DOFs constrained is counted as the number of underconstraints for each feasible joint assignment and recorded as .…”

Section: Decomposition Rule For Dimensional Integritymentioning

confidence: 99%

“…The union of screw matrices represents the sum of the screw spaces defined by the matrices and can be obtained by simply "stacking" them on top of one another (4) 2 The terminology and formalization in this section are summarized from [6], [15], [17]- [19]. The intersection of screw matrices is the set of screws common to the screw matrices and can be computed through double reciprocals (5) Since a twist and a wrench are also screws, the definitions of reciprocal, union, and intersection hold.…”

Section: Screw Theorymentioning

confidence: 99%

“…There is an important exception to (15), for which compensation should be made before it is checked against (15); when there are connections in , from multiple fixture element to one member, the wrench matrices associated with the connections should be combined as a union such that the intersection among them could be ignored. This is based on a basic assumption that there would be no overconstraint between a fixture and a member.…”

Section: Decomposition Rule For Dimensional Integritymentioning

confidence: 99%

“…Blanding [4] showed the application of Screw Theory to assembly design. Adams and Whitney [15] also used Screw Theory to compute 1 A fixture scheme is defined as a plan showing which fixture will control what critical dimensions where in assembly sequence. More formal definition will follow in terminology section.…”

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Integrated Synthesis of Assembly and Fixture Scheme for Properly Constrained Assembly

Lee

2004

Volume 3d: 8th Design for Manufacturing Conference

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Abstract-This paper presents an integrated approach to design an assembly, fixture schemes, and an assembly sequence, such that the dimensional integrity of the assembly is insensitive to the dimensional variations of individual parts. The adjustability of critical dimensions and the proper constraining of parts during assembly process are the keys in achieving the dimensional integrity of the final assembly. A top-down design method is developed which recursively decomposes a lump of initial product geometry and fixture elements matching critical dimensions into parts and fixtures. At each recursion, joints are assigned to the interfaces between two subassemblies to ensure that parts and fixtures are properly constrained at every assembly step. A case study on a simple frame structure is presented to demonstrate the method.Note to Practitioners-Achieving dimensional integrity of complex assemblies is a very demanding task due to the dimensional variations of parts and their propagation. Keys to achieving the goal are to adjust critical dimensions using proper fixtures and joint configurations and to minimize unpredictable deformations caused by overconstrained parts, such that assembled products can be robust to dimensional variations of parts. Equally important are arranging fixtures and sequencing assembly steps as these are what really define which critical dimension is adjusted and which subassemblies are put together on what fixture at each assembly step. In this paper, we propose a top-down decomposition-based approach that generates assembly design, assembly sequence, and fixture plan ensuring adjustability for critical dimensions and properly constrained subassemblies at every assembly step. The method does not only prevent costly trial and error following bottom-up approaches, but also enumerates all feasible solutions for a given product geometry and critical dimensions. As the number of solutions can be fairly large, for real-word application, it is crucial to incorporate practical constraints and to identify other important criteria to search optimal designs. Index Terms-Assembly synthesis, design for manufacture, dimensional integrity, proper constraint.

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Section: Decomposition Rule For Dimensional Integritymentioning

confidence: 99%

Section: Screw Theorymentioning

confidence: 99%

Section: Decomposition Rule For Dimensional Integritymentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Integrated Synthesis of Assembly and Fixture Scheme for Properly Constrained Assembly

Lee

2004

Volume 3d: 8th Design for Manufacturing Conference

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show abstract

“…Huang and Schimmels [24,25] studied the realization of a prescribed stiffness matrix with serial or parallel elastic mechanisms. Other applications of screw theory include mobility analysis [26], assembly analysis [27,28] and topology synthesis [29]. Recently Kim [30] studied the characterization of compliant building blocks by utilizing the concept of eigentwists and eigenwrenches based on screw theory.…”

Section: Introductionmentioning

confidence: 99%

A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

Dorozhkin

Vance

2009

Volume 7: 33rd Mechanisms and Robotics Conference, Parts a and B

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This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraintbased approach for the synthesis and analysis of compliant mechanisms. NOMENCLATURE Ω Ω Ω A 3D vector presenting the angular velocity of a twist V A 3D vector presenting the linear velocity of a twist p A scalar representing the pitch of a twist T A 6D general twist representing an allowable motion ∏ T A twist matrix representing the allowable motion space F A 3D vector presenting the force part of a wrench * Address all correspondence to this author.M A 3D vector presenting the couple part of a wrench q A scalar representing the pitch of a wrencĥ W A 6D general wrench representing a constraint ∏ W A wrench matrix representing the constraint space IntroductionCompared with traditional rigid body mechanisms, compliant mechanisms [1] or flexures have many advantages, such as high precision and a simplified manufacturing and assembly process. However the design and analysis of compliant mechanisms is complex due to the nonlinearity of deformation of the flexible members. Researchers in two isolated fields, kinematics and mechanisms and precision engineering, have independently made major contributions to compliant mechanism design.In the kinematics and mechanisms community, research has focused on applying computational techniques to determine the dimensions and/or topologies of compliant mechanisms to achieve a pre-specified design objective. The two most often used approaches in this field are the Pseudo-Rigid-Body-Model (PRBM) [2] approach and the topological synthesis approach [3][4][5][6][7][8]. The former approach models a compliant mechanism as a rigid body with one or more springs. These springs impose approximated lumped compliance to the rigid link models of compliant mechanisms. This allows the theories and methodologies developed for rigid body mechanisms [9,10] to be used to design compliant mechanisms. Because of this simplification in the modeling process, it is necessary to evaluate the designs to ensure

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A Unified Approach to Design of Assemblies Integrating Nominal and Variation Design

Whitney

Models for Computer Aided Tolerancing in Design and Manufacturing

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Application of Screw Theory to Constraint Analysis of Mechanical Assemblies Joined by Features

Cited by 53 publications

References 18 publications

Integrated Synthesis of Assembly and Fixture Scheme for Properly Constrained Assembly

Integrated Synthesis of Assembly and Fixture Scheme for Properly Constrained Assembly

A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

A Unified Approach to Design of Assemblies Integrating Nominal and Variation Design

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