Rigid body dynamics using equimomental systems of point-masses

Abstract The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work, the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four-dimensional modulo-permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point-masses at infinity is also investigated. Applications of these ideas to rigid body dynamics are considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation.

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A Measurement Oriented Formulation of the Dynamics of Natural and Robotic Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2896424 ◽

1991 ◽

Vol 113 (3) ◽

pp. 401-408 ◽

Cited By ~ 1

Author(s):

H. Hemami

Keyword(s):

Rigid Body ◽

Inverse Dynamics ◽

Rigid Body Dynamics ◽

Moment Of Inertia ◽

Computational Burden ◽

Inertia Matrix ◽

Body Dynamics ◽

Sensory Modalities ◽

On Line ◽

Internal Forces

A measurement oriented formulation of rigid body dynamics is applied to a special class of planar linkage systems. It leads to a diagonal moment of inertia matrix, and thus simplifies the feedforward computations in the controller. On the other hand, if measurements are not available or measurements are not allowed, the computational burden shifts to the feedback computation of the generalized or internal forces. This formulation may find applications in off-line digital computer simulations and on-line control of the rigid body systems via the inverse dynamics methods. It may also underly computations in natural and biological systems that are rich with sensory modalities and processes. The computational burden in this model is shifted from the inverse of moment of inertia matrix to the derivation of the forces of constraint, contact, connection, internal or generalized. When these forces are available from measurements, the computations are indeed reduced and consequently on-line control problems are rendered easier. As a consequence of this representation the problems of transmission delay, and predictive compensation become important as is shown via an example. The investigation of the range of intermediate representations where computations and measurements are combined remains a fertile subject.

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Slipping–rolling transitions of a body with two contact points

Nonlinear Dynamics ◽

10.1007/s11071-021-06538-5 ◽

2021 ◽

Author(s):

Mate Antali ◽

Gabor Stepan

Keyword(s):

Rigid Body ◽

Contact Point ◽

Static Friction ◽

Rigid Body Dynamics ◽

Contact Forces ◽

Friction Forces ◽

Contact Points ◽

Body Dynamics ◽

Coulomb Model ◽

Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

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