Research Papers

Analysis of Constraint Configurations in Mechanical Assembly via Screw Theory

[+] Author and Article Information
Leonard Rusli

Research EngineerDepartment of Mechanical and Aerospace Engineering,The Ohio State University,United States,201 W. 19th Ave.Columbus, OH 43210rusli.10@osu.edu

Anthony Luscher

Associate ProfessorDepartment of Mechanical and Aerospace EngineeringThe Ohio State University201 W. 19th Ave.Columbus, OH 43210 United Statesluscher.3@osu.edu

James Schmiedeler

Associate ProfessorDepartment of Aerospace and Mechanical Engineering,University of Notre Dame,365 Fitzpatrick Hall,Notre Dame, IN 46556, United Statesschmiedeler.4@nd.edu

J. Mech. Des 134(2), 021006 (Feb 03, 2012) (12 pages) doi:10.1115/1.4005622 History: Received June 22, 2011; Revised December 12, 2011; Published February 03, 2012

The essential function of a mechanical assembly is the removal of degrees of freedom (DOF) to enable the transfer of load between two bodies. Assembly constraint features serve to provide this DOF removal, so their locations and orientations greatly affect the quality of an assembly as measured by its ability to resist relative motion between the parts. This paper addresses attachment-level design in which design decisions are made to establish the types, locations, and orientations of assembly features. The analysis methodology in this paper models assembly features such as point, pin, line, and plane constraints with equivalent first, second, and third order wrench systems. The set of relative motions to be evaluated is generated by composing from among these constraints a five-system pivot wrench combination to which a freedom screw motion is reciprocal. The effectiveness of each constraint to resist these motions is calculated as the ratio of the reaction forces at each resisting constraint to the input wrench magnitude. Based on these resistance values, multiple rating metrics are calculated to rate the overall assembly’s performance in resisting the motion. This work represents the first tool available to analyze a constraint configuration’s effectiveness to resist motion with a quantitative metric. Case studies are presented to demonstrate the utility of the analysis tool.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Assembly constraint strategy using various features

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Figure 2

Representing pin contact as many unilateral contacts

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Figure 3

Overall methodology algorithm

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Figure 4

(a) Pin constraint; (b) pin wrench equivalent

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Figure 5

(a) Line constraint; (b) second special 2-system wrench representation; (c) when hα=0,hβ=∞

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Figure 6

(a) Plane constraint; (b) seventh special 3-system wrench representation; (c) when hα=0,hβ=h∞=∞

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Figure 7

Comparison of isolated reaction force versus virtual displacement model

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Figure 8

Isolated reaction force model equilibrium

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Figure 9

The input wrench represented as a force couple

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Figure 10

Input wrench magnitude versus (a) screw pitch and (b) wrench pitch

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Figure 11

ECD geometry constraint configuration and WSR motion

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Figure 12

Endcap geometry and constraint configuration

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Figure 13

Generic cube constraint configuration




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