A matrix formulation for the dynamic analysis of spatial mechanisms using point coordinates and velocity transformation.

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Bibliographic Details
Title:	A matrix formulation for the dynamic analysis of spatial mechanisms using point coordinates and velocity transformation.
Authors:	Attia, H. A.¹
Source:	Acta Mechanica. 2003, Vol. 165 Issue 3-4, p207-222. 16p.
Subjects:	Matrix groups, Dynamics, Speed, Kinematics
Abstract:	This paper presents a matrix formulation for the dynamic analysis of spatial mechanisms with Common types of kinematic joints. The formulation is derived in two steps. Initially an equivalent constrained system of particles that replaces the rigid bodies is constructed and used to define the configuration of the mechanical system. This results in a simple and straightforward procedure for generating the equations of motion in terms of the rectangular Cartesian coordinates of the particles without introducing any rotational coordinates. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates the relative joint velocities to the Cartesian velocities. For the open loop case, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For the closed loop case, suitable joints should be cut and few cut-joints constraint equations should be included for each closed loop. An example is used to demonstrate the generality and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This paper presents a matrix formulation for the dynamic analysis of spatial mechanisms with Common types of kinematic joints. The formulation is derived in two steps. Initially an equivalent constrained system of particles that replaces the rigid bodies is constructed and used to define the configuration of the mechanical system. This results in a simple and straightforward procedure for generating the equations of motion in terms of the rectangular Cartesian coordinates of the particles without introducing any rotational coordinates. The equations of motion are then derived in terms of relative joint coordinates through the use of a velocity transformation matrix. The velocity transformation matrix relates the relative joint velocities to the Cartesian velocities. For the open loop case, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For the closed loop case, suitable joints should be cut and few cut-joints constraint equations should be included for each closed loop. An example is used to demonstrate the generality and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]
ISSN:	00015970
DOI:	10.1007/s00707-003-0027-4