On the Computation of Relative Rotations and Geometric Phases in the Motions of Rigid Bodies

1997 ◽  
Vol 64 (4) ◽  
pp. 969-974 ◽  
Author(s):  
O. M. O’Reilly
Keyword(s):  
Rigid Body ◽  
Computational Methods ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Relative Rotation ◽  
Geometric Phases ◽  
Body Dynamics ◽  
Computational Aspects ◽  
Body Rolling ◽  
The Moment

In this paper, expressions are established for certain relative rotations which arise in motions of rigid bodies. A comparison of these results with existing relations for geometric phases in the motions of rigid bodies provides alternative expressions of, and computational methods for, the relative rotation. The computational aspects are illustrated using several examples from rigid-body dynamics: namely, the moment-free motion of a rigid body, rolling disks, and sliding disks.

Analysis of rigid-body dynamics for closed-loop mechanisms—its application to a novel satellite tracking device

2003 ◽  
Vol 217 (4) ◽  
pp. 285-298
Author(s):  
T P Jones ◽  
G R Dunlop
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Satellite Tracking ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Parallel Mechanisms ◽  
Body Dynamics ◽  
Tracking Device ◽  
General Method

A general method for analysing the velocity and acceleration kinematics of parallel mechanisms is introduced. A method for analysing the forces experienced by rigid bodies in parallel mechanisms is then introduced, which builds on the kinematics that result in a solution to the dynamics of rigid bodies in parallel mechanisms.

On Analytical Evaluation of Gear Dynamic Factors Based on Rigid Body Dynamics

1985 ◽  
Vol 107 (2) ◽  
pp. 301-311 ◽  
Author(s):  
C. C. Wang
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Time Derivative ◽  
Transmission Error ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Dynamic Factor ◽  
Lumped Mass ◽  
Body Dynamics ◽  
Cubic Spline Curve

This paper proposes an initial step to rationalize the dynamic factor calculation and bring it under the control of the laws of mechanics. The theory is straight forward. The concept of mathematical scaling is utilized to simplify the system dynamics’ formulation. The rigid body dynamics accounts for the gear dynamic tooth loads resulting from the prescribed transmission error of each gear step—including the artificial ones. The latter converts a lumped-mass-elastic system into a rigid-bodies-transmission-error system subjected to the solution of the rigid body system dynamics according to Newton’s law. The entire concept of the solution has been implemented into a FORTRAN program approximately 600 statements in length. The results obtained through computer simulation of various test cases demonstrate the potential and effectiveness of the proposed concept. Contrary to the current practice of grossly ignoring the inertial and system effects, this paper has taken all these important factors into account. The transmission-error-induced acceleration is approximated by the second-order time derivative of one of the cubic spline curve-fitting methods. The approach is cost effective and numerically satisfactory. The model can be further improved to reduce the extent of basic assumptions, or to increase the number of conditional constraints without losing economical attractiveness.

Predicting Rebounds Using Rigid-Body Dynamics

1991 ◽  
Vol 58 (3) ◽  
pp. 754-758 ◽  
Author(s):  
Charles E. Smith
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
System Of Rigid Bodies ◽  
Body Dynamics

The observation by Thomas Kane a few years ago, that long-used relationships for predicting post-collision motion of a system of rigid bodies can imply a significant increase in kinetic energy during collision, has revived interest in this type of problem. This paper is intended to clarify understanding of the sources of this difficulty, and to suggest an alternative to some of the previously used assumptions for making such predictions. An organization of the pertinent equations of kinetics is presented, which provides a more direct means of examining the aforementioned question and of obtaining rebound predictions.

Dynamics of General Constrained Robots Derived from Rigid Bodies

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Wen-Hong Zhu
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Joint Space ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Configuration Spaces ◽  
Task Space ◽  
Body Dynamics ◽  
Constrained Robots

A systematic approach for deriving the dynamical expression of general constrained robots is developed in this paper. This approach uses rigid-body dynamics and two kinematics-based mapping matrices to form the dynamics of complex robots in closed form. This feature enables the developed modeling approach to be rigorous in nature, since every actuator and gear-head can be separated into rigid bodies and no assumption about approximation beyond rigid-body dynamics is made. The two kinematics-based mapping matrices are used to govern the velocity and force transformations among three configuration spaces, namely, general joint space, general task space, and extended subsystems space. Consequently, the derived dynamics of general constrained robots maintain the same form and main properties as the conventional single-arm constrained robots. This approach is particularly useful for robots with hyper degrees of freedom. Five examples are given.

Addenda to “On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models”

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Inertial Frame ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Coordinate Systems ◽  
Body Frame ◽  
Modeling And Analysis ◽  
Body Dynamics

Although quaternions are singularity-free in modeling and analysis of rigid bodies in three-dimensional motion, description of torques may lead to unbounded response of a quaternion-based model. This paper gives theorems on the conditions of torque-induced singularity in four coordinate systems: inertial frame, body frame, Euler basis, and dual Euler basis. According to the theorems, torques applied in an inertial frame or a body frame or a Euler basis will never cause unbounded motion; torques applied in a dual Euler basis, however, may lead to unbounded motion.

On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Applied Torque ◽  
Body Dynamics

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed.

scholarly journals Mesoscopic Rigid Body Modelling of the Extracellular Matrix Self-Assembly

2018 ◽  
Vol 15 (2) ◽  
Author(s):  
Hua Wong ◽  
Jessica Prévoteau-Jonquet ◽  
Stéphanie Baud ◽  
Manuel Dauchez ◽  
Nicolas Belloy
Keyword(s):  
Extracellular Matrix ◽  
Rigid Body ◽  
Self Assembly ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Biological Molecules ◽  
Body Dynamics ◽  
Technological Limitations ◽  
Insight Into ◽  
Prime Target

AbstractThe extracellular matrix (ECM) plays an important role in supporting tissues and organs. It even has a functional role in morphogenesis and differentiation by acting as a source of active molecules (matrikines). Many diseases are linked to dysfunction of ECM components and fragments or changes in their structures. As such it is a prime target for drugs. Because of technological limitations for observations at mesoscopic scales, the precise structural organisation of the ECM is not well-known, with sparse or fuzzy experimental observables. Based on the Unity3D game and physics engines, along with rigid body dynamics, we propose a virtual sandbox to model large biological molecules as dynamic chains of rigid bodies interacting together to gain insight into ECM components behaviour in the mesoscopic range. We have preliminary results showing how parameters such as fibre flexibility or the nature and number of interactions between molecules can induce different structures in the basement membrane. Using the Unity3D game engine and virtual reality headset coupled with haptic controllers, we immerse the user inside the corresponding simulation. Untrained users are able to navigate a complex virtual sandbox crowded with large biomolecules models in a matter of seconds.

scholarly journals A Simple Treatment of Constraint Forces and Constraint Moments in the Dynamics of Rigid Bodies

2014 ◽  
Vol 67 (1) ◽  
Author(s):  
Oliver M. O'Reilly ◽  
Arun R. Srinivasa
Keyword(s):  
Rigid Body ◽  
Classical Mechanics ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Constraint Forces ◽  
Simple Treatment ◽  
Body Dynamics ◽  
Expository Article

In this expository article, a simple concise treatment of Lagrange's prescription for constraint forces and constraint moments in the dynamics of rigid bodies is presented. The treatment is suited to both Newton–Euler and Lagrangian treatments of rigid body dynamics and is illuminated with a range of examples from classical mechanics and orthopedic biomechanics.

scholarly journals Slipping–rolling transitions of a body with two contact points

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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