Minimal Fixturing of Frictionless Assemblies: Complexity and Algorithms

Baraff, David; Mattikalli, Raju; Khosla, Pradeep K.

doi:10.1007/pl00014419

Cited by 17 publications

(13 citation statements)

References 18 publications

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“…An assembly is first-order stable if all kinematically possible virtual displacements of the system result in a strict positive increase in potential energy of the system. First-order stability is equivalent to robust directional equilibrium for a system of rigid bodies and their fixtures, as formulated by Baraff et al [3]. Our definition of stability is equivalent to directional equilibrium of Baraff et al [3] and weak stability of Pang and Trinkle [28], which are defined to hold for an assembly if the contact forces that arise in response to an external force exactly balance the external force and induce zero body accelerations.…”

Section: A Stability Analysismentioning

confidence: 98%

The Influence of Motion Paths and Assembly Sequences on the Stability of Assemblies

Rakshit

Akella

2015

IEEE Trans. Automat. Sci. Eng.

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In this paper, we present an approach for the stability analysis of mechanical part disassembly considering part motion in the presence of physical forces such as gravity and friction. Our approach uses linear complementarity to analyze stability as parts are moved out of the assembly. As each part is removed from the assembly along a specified path during disassembly, we compute the contact forces between parts in the remaining assembly; positive contact forces throughout the disassembly process imply the disassembly sequence is stable (since the parts remain in contact with one another). However, if the part that is being taken out induces motion of other parts in the remaining subassembly, we conclude the disassembly sequence is unstable. Thus, we are able to simulate the entire disassembly considering physical forces and part motion, which has not previously been done. We then show the influence of part motion on stable disassembly. In contrast to prior work on disassembly that has focused either on planning part motions based on only geometric constraints, or on analyzing the stability of an assembly without considering part motions, we explore the relation between part motion and the selection of stable disassembly sequences in 2-D and 3-D. We establish conditions that characterize path-dependent assemblies, where motion paths can play a significant role in stable disassembly. Since we track the motion of all parts in an assembly, instability inducing motions can be identified and prevented by introducing appropriate fixtures by selecting alternative disassembly sequences or by changing the motion paths. We extend the stability analysis for single part disassembly to stability analysis of subassembly disassembly. We additionally show that in the presence of friction, assembly and disassembly can be noninvertible.Note to Practitioners-Maintaining the stability of an assembly as assembly or disassembly proceeds is critical during product assembly, repair, and maintenance. While fixtures can ensure stability, they add cost and restrict access for parts and tools. We show that the stability of the assembly can depend on the paths taken by the parts, and present an approach for selecting paths that ensure stability from among the geometrically feasible paths. The main application is in assembly and disassembly planning for reducing the fixturing requirements and in planning assembly motions that do not cause instability. The results will also be useful in designing disassembly operations during maintenance or repair, when it may not be possible to fixture all parts. The stability analysis can also be used by assistive robots in domestic environments for tasks like Manuscript stacking objects and for safe removal of collapsed structures after disasters such as earthquakes.

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Section: A Stability Analysismentioning

confidence: 98%

The Influence of Motion Paths and Assembly Sequences on the Stability of Assemblies

Rakshit

Akella

2015

IEEE Trans. Automat. Sci. Eng.

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“…We would like to thank one of the reviewers for comments and bringing the work in Baraff, Mattikalli, and Khosla (1997) to our attention. Joskowicz is supported by grant 98/536 from the Israeli Academy of Science and by a grant from the Authority for Research and Development, The Hebrew University of Jerusalem, Israel.…”

Section: Acknowledgmentsmentioning

confidence: 98%

“…Linear constraints and linear programming techniques have been proposed for stability analysis (Wolter and Trinkle 1994;Baraff, Mattikalli, and Khosla 1997): given an assembly of parts, determine from the part placements and (a) (b) Fig. 1.…”

Section: Previous Workmentioning

confidence: 99%

“…Using mixed-integer programming techniques, as proposed in Wolter and Trinkle (1994), has a much higher computational cost. The algorithm for solving the system of constraints in Baraff, Mattikalli, and Khosla (1997) requires all variables to be strictly positive. This is overly restrictive for m-handed assembly since some variables may have to be negative or zero to model parts at rest.…”

Section: Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Linear Unboundedness Testing: Algorithm and Applications to Translational Assembly Planning

Schwarzer¹,

Schweikard

Joskowicz

2000

The International Journal of Robotics Research

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We address the problem of efficiently testing for linear unboundedness and its applications to translational assembly planning. We describe a new algorithm that performs the test by solving a single homogeneous system of equations followed by a single linear feasibility test. We show that testing for unboundedness is computationally at least as hard as these two subproblems. The new algorithm is the fastest known algorithm and is practical. We then present a framework for general translational assembly planning based on linear constraints. We show the relation of m-handed assembly planning to unboundedness testing and present a polynomialtime algorithm for m-handed assembly of polygonal part assemblies with no initially separated pairs of parts. For the general translational assembly-planning problem, we present a new algorithm that uses unboundedness testing and a cell reduction technique to significantly increase the search efficiency. Experimental results of our implementation on a variety of planar and spatial assemblies demonstrate the practicality of the algorithms.

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“…Mattikalli et al [11] extended that work to find all stable orientations of assemblies with friction. Baraff et al [1] proposed methods to design three different types of fixtures for frictionless assemblies of polyhedra. A fixture that provides directional stability balances a given external wrench exactly.…”

Section: A Related Workmentioning

confidence: 99%

Stable Pushing of Assemblies

Bernheisel

Lynch

Proceedings of the 2005 IEEE International Conference on Robotics and Automation

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This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible) any force necessary to assure stability of the assembly can be generated by the pushing contacts; (I = impossible) stability of the assembly is impossible; and (U = undecided) pushing forces may or may not be able to stabilize the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the pushing contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given.

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Minimal Fixturing of Frictionless Assemblies: Complexity and Algorithms

Cited by 17 publications

References 18 publications

The Influence of Motion Paths and Assembly Sequences on the Stability of Assemblies

The Influence of Motion Paths and Assembly Sequences on the Stability of Assemblies

Efficient Linear Unboundedness Testing: Algorithm and Applications to Translational Assembly Planning

Stable Pushing of Assemblies

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