Application of screw theory to motion analysis of assemblies of rigid parts

Adams, Jeffrey; Gerbino, Salvatore; Whitney, Daniel E.

doi:10.1109/isatp.1999.782938

Cited by 12 publications

(5 citation statements)

References 28 publications

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“…A user can combine members of this set to join two parts, and then determine whether or not the defined feature set over-, under-, or fully-constrains the location and orientation of the part. Motion limit analysis [74] uses the mathematics of screw theory to model the ability of assembly features to allow or constrain rigid body motions in six DOF. The directions and quantitative amounts of possible finite rigid body motions of a part that is being added to an assembly can be determined via calculation applied to a defined set of assembly features.…”

Section: Screw Theory Basedmentioning

confidence: 99%

Relation between part position and kinematic freedom: An expository survey

Dawari

Sen

2010

Mechanism and Machine Theory

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Section: Screw Theory Basedmentioning

confidence: 99%

Relation between part position and kinematic freedom: An expository survey

Dawari

Sen

2010

Mechanism and Machine Theory

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“…Waldron [22] utilized the Screw Theory to build a general method to determine all relative degrees of freedom (DOF) between two rigid bodies making contacts to each other. Extending the work by Konkar and Cutkosky [23], Adams and Whitney [24,25] developed a method to determine the status (over-, under-or fully constrained) of rigid body assemblies with mating features. Their method also determines the motion type and range of under-constrained rigid body assemblies.…”

Section: Screw Theory In Motion and Constraint Analysismentioning

confidence: 99%

Design for Disassembly With High-Stiffness Heat-Reversible Locator-Snap Systems

Crowther¹

2008

Journal of Mechanical Design

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Recent legislative and social pressures have driven manufacturers to consider effective part reuse and material recycling at the end of product life at the design stage. One of the key considerations is to design and use joints that can disengage with minimum labor, part damage, and material contamination. This paper presents a unified method to design a high-stiffness reversible locator-snap system that can disengage nondestructively with localized heat, and its application to external product enclosures of electrical appliances. The design problem is posed as an optimization problem to find the locations, numbers, and orientations of locators and snaps as well as the number, locations, and sizes of heating areas, which realize the release of snaps with minimum heating area and maximum stiffness while satisfying any motion and structural requirements. The screw theory is utilized to precalculate a set of feasible orientations of locators and snaps, which are examined during optimization. The optimization problem is solved using the multi-objective genetic algorithm coupled with the structural and thermal finite element analysis. The method is applied to a two-piece enclosure of a DVD player with a T-shaped mating line. The resulting Pareto-optimal solutions exhibit alternative designs with different trade-offs between the structural stiffness during snap engagement and the area of heating for snap disengagement. Some results require the heating of two areas at the same time, demonstrating the idea of a lock-and-key.

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“…Konkar and Cutkosky [14] created screw system representations of assembly mating features. Adams et al [15][16][17] used Konkar's algorithm and extended their work by defining extensible screw representations of some types of assembly features. Gerbino et al [18,19] proposed an algorithm to decompose the liaison diagram representing an assembly into simple paths, to which the application of the twist union or intersection algorithms may be easily applied.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, it is time consuming when the machine is large and complex. On the other hand, to determine the screw system by using the methods proposed in [14][15][16][17][18][19][20][21][22], all of the screw representations of different features that may be used first have to be modeled. This is awkward and resembles geometric reasoning [30].…”

Section: Introductionmentioning

confidence: 99%

Recognition of Kinematic Joints of 3D Assembly Models Based on Reciprocal Screw Theory

Xiong

Chen

Ding

et al. 2016

Mathematical Problems in Engineering

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Reciprocal screw theory is used to recognize the kinematic joints of assemblies restricted by arbitrary combinations of geometry constraints. Kinematic analysis is common for reaching a satisfactory design. If a machine is large and the incidence of redesign frequent is high, then it becomes imperative to have fast analysis-redesign-reanalysis cycles. This work addresses this problem by providing recognition technology for converting a 3D assembly model into a kinematic joint model, which is represented by a graph of parts with kinematic joints among them. The three basic components of the geometric constraints are described in terms of wrench, and it is thus easy to model each common assembly constraint. At the same time, several different types of kinematic joints in practice are presented in terms of twist. For the reciprocal product of a twist and wrench, which is equal to zero, the geometry constraints can be converted into the corresponding kinematic joints as a result. To eliminate completely the redundant components of different geometry constraints that act upon the same part, the specific operation of a matrix space is applied. This ability is useful in supporting the kinematic design of properly constrained assemblies in CAD systems.

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Application of screw theory to motion analysis of assemblies of rigid parts

Cited by 12 publications

References 28 publications

Relation between part position and kinematic freedom: An expository survey

Relation between part position and kinematic freedom: An expository survey

Design for Disassembly With High-Stiffness Heat-Reversible Locator-Snap Systems

Recognition of Kinematic Joints of 3D Assembly Models Based on Reciprocal Screw Theory

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