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A simplified recursive formulation for the dynamic analysis of spatial mechanisms in point coordinates
Author(s) -
Attia H.A.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310049
Subject(s) - revolute joint , cartesian coordinate system , log polar coordinates , generalized coordinates , action angle coordinates , kinematics , orthogonal coordinates , simple (philosophy) , coordinate system , chain (unit) , point (geometry) , equations of motion , transformation matrix , rotation (mathematics) , motion (physics) , homogeneous coordinates , rigid body , rotation around a fixed axis , transformation (genetics) , matrix (chemical analysis) , mathematics , classical mechanics , mathematical analysis , geometry , physics , constraint (computer aided design) , philosophy , biochemistry , chemistry , epistemology , astronomy , materials science , composite material , gene
In the present study, a recursive formulation for generating the equations of motion of spatial mechanisms with revolute and/or spherical joints is presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. It eliminates the necessity of distributing the external forces and couples over the equivalent system of particles. For the open‐chain system, the equations of motion are generated recursively along the serial chains. Closed‐chain system is transformed to open‐chain by cutting suitable kinematic joints and introducing cut‐joint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.