Simulation of dynamics of interacting rigid bodies including friction I: General problem and contact model

Goyal, Siddharth; Pinson, Elliot N.; Sinden, Frank W.

doi:10.1007/bf01198742

Cited by 60 publications

(32 citation statements)

References 15 publications

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“…Such collisional contact constitutive assumptions fall into three main classes: fulldeformation laws; incremental laws (also called "soft"); and algebraic laws (also called "hard" -see Goyal et al, 1994;Walton, 1992). Full-deformation laws are based on continuum mechanics equations for the whole body, most often linear elasto-dynamic equations.…”

Section: Introductionmentioning

confidence: 99%

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

Chatterjee

Ruina

1998

Journal of Applied Mechanics

176

167

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We present a geometric representation of the set of 3D rigid body collisional impulses that are reasonably permissible by the combination of non-negative post-collision separation rate, non-negative collisional compression impulse, non-negative energy dissipation and the Coulomb friction inequality. The construction is presented for a variety of special collisional situations involving special symmetry or extremes in the mass distribution, the friction coefficient, or the initial conditions. We review a variety of known friction laws and show how they do and do not fit in the permissible region in impulse space as well as comment on other attributes of these laws. We present a few parameterizations of the full permissible region of impulse space. We present a simple generalization to arbitrary 3D point contact collisions of a simple law previously only applicable to objects with contact-inertia eigenvectors aligned with the surface normal and initial relative tangent velocity component (e.g. spheres and disks). This new algebraic collision law has two restitution parameters for general 3D frictional single-point rigidbody collisions. The new law generates a collisional impulse that is a weighted sum of the impulses from a frictionless but non-rebounding collision and from a perfectly sticking, non-rebounding collision. We describe useful properties of our law; show geometrically the set of impulses it can predict for several collisional situations; and compare it with existing laws. For simultaneous collisions we propose that the new algebraic law be used by recursively breaking these collisions into a sequence ordered by the normal approach velocities of potential contact pairs.

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Section: Introductionmentioning

confidence: 99%

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

Chatterjee

Ruina

1998

Journal of Applied Mechanics

176

167

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“…Hence, their accelerations are rapid and so are the contact forces [20,21]. It is assumed that the positions of the contact nodes remain unchanged during collision.…”

Section: The External Contact Model Of the Robotmentioning

confidence: 99%

“…Substituting the above terms, the Jacobian and the contact force into (20) gives the dynamic equation of the motion of a 12-tetrahedron robot, which has the same form as that of a general parallel robot. M Q is not a diagonal matrix, there are inertial couplings between the nodes and between the struts.…”

Section: The External Contact Model Of the Robotmentioning

confidence: 99%

Dynamical Modelling and a Decentralized Adaptive Controller for a 12-Tetrahedral Rolling Robot

Wang

Zhang

2018

TFAMENA

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SummaryThe 12-tetrahedral robot is an addressable reconfigurable technology (ART)-based variable geometry truss mechanism with twenty-six extensible struts and nine nodes arranged in a tetrahedral mesh. The robot has the capability of reconfiguring shape and dimension for environment sensing requirements, which makes it suitable for space exploration and environmental perception. In this paper, we have derived a dynamics model and presented a decentralized adaptive controller for a 12-tetrahedral robot. First, the robot is divided into the node and the strut subsystems, and the kinetic and the potential energy are calculated for the two subsystems. Then, the dynamics model is achieved by applying the Lagrangian formalism on the total energy of the robot. Since the dynamics is too complicated for implementing model-based controllers, a two-layer controller is presented to control the robot, in which the planning layer determines gait and trajectory of the robot, and the executive layer adopts the decentralized adaptive control strategy and consists of twenty-six strut controllers. Each strut controller regulates the movement of the corresponding strut without information exchange with other struts. Co-simulations based on ADAMS and Matlab have been conducted to verify the feasibility and effectiveness of the proposed controller.

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“…Goyal [7] and Kraus [29] derive models for frictional impacts from compliance models as alternatives to rigid-body impact models developed by Brach [30], Chaterjee and Ruina [31], and Mirtich [32]. Marghitu and Hurmuzlu employ continuum models for the study of frictional impacts [33].…”

Section: Introductionmentioning

confidence: 99%

A semi‐implicit time‐stepping model for frictional compliant contact problems

Song

Pang

Kumar

2004

Numerical Meth Engineering

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SUMMARYIn this paper, we formulate a semi-implicit time-stepping model for multibody mechanical systems with frictional, distributed compliant contacts. Employing a polyhedral pyramid model for the friction law and a distributed, linear, viscoelastic model for the contact, we obtain mixed linear complementarity formulations for the discrete-time, compliant contact problem. We establish the existence and finite multiplicity of solutions, demonstrating that such solutions can be computed by Lemke's algorithm. In addition, we obtain limiting results of the model as the contact stiffness tends to infinity. The limit analysis elucidates the convergence of the dynamic models with compliance to the corresponding dynamic models with rigid contacts within the computational time-stepping framework. Finally, we report numerical simulation results with an example of a planar mechanical system with a frictional contact that is modelled using a distributed, linear viscoelastic model and Coulomb's frictional law, verifying empirically that the solution trajectories converge to those obtained by the more traditional rigid-body dynamic model.

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Simulation of dynamics of interacting rigid bodies including friction I: General problem and contact model

Cited by 60 publications

References 15 publications

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations

Dynamical Modelling and a Decentralized Adaptive Controller for a 12-Tetrahedral Rolling Robot

A semi‐implicit time‐stepping model for frictional compliant contact problems

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