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Research Papers

A Recursive Hybrid Time-Stepping Scheme for Intermittent Contact in Multi-Rigid-Body Dynamics

[+] Author and Article Information
Kishor D. Bhalerao1

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180bhalek@rpi.edu

Kurt S. Anderson

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180anderk5@rpi.edu

Jeffrey C. Trinkle

Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180trink@cs.rpi.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 4(4), 041010 (Aug 25, 2009) (11 pages) doi:10.1115/1.3192132 History: Received August 22, 2008; Revised October 23, 2008; Published August 25, 2009

This paper describes a novel method for the modeling of intermittent contact in multi-rigid-body problems. We use a complementarity based time-stepping scheme in Featherstone’s divide and conquer framework to efficiently model the unilateral and bilateral constraints in the system. The time-stepping scheme relies on impulse-based equations and does not require explicit collision detection. A set of complementarity conditions is used to model the interpenetration constraint and a linearized friction cone is used to yield a linear complementarity problem. The divide and conquer framework ensures that the size of the resulting mixed linear complementarity problem is independent of the number of bilateral constraints in the system. This makes the proposed method especially efficient for systems where the number of bilateral constraints is much greater than the number of unilateral constraints. The method is demonstrated by applying it to a falling 3D double pendulum.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Proximal points between two convex bodies

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Figure 2

Polygonal approximation of the circular friction cone (10)

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Figure 3

The hierarchic assembly and disassembly processes using binary-tree structure

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Figure 4

Representative bodies of a multibody system

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Figure 5

Assembly process for a unilateral constraint on body k

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Figure 6

Unilateral constraint is defined between the xy plane and point P1 on body A

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Figure 7

Drift in x and y coordinates of the center of mass of the double pendulum for μ=0

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Figure 8

Comparison between the time-stepping scheme and AUTOLEV model

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Figure 9

x and z coordinates of point P1 for a planar (xz) double pendulum

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Figure 10

Elastic contact between point P1 and xy plane, ϵN=0.7

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