Accelerations in the Ball Joint

A procedure for calculating relative accelerations in spatial mechanisms is extended to include ball joints. The relationship of the relative velocities in a closed-loop mechanism is differentiated and then manipulated into set of simultaneous linear equations in the unknown relative accelerations....

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Bibliographic Details
Published in:Mechanics based design of structures and machines 2014-01, Vol.42 (1), p.1-16
Main Author: Fischer, Ian S.
Format: Article
Language:English
Subjects:
Acceleration
Ball joint
Dual number
Relative acceleration
RSSR
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Summary:A procedure for calculating relative accelerations in spatial mechanisms is extended to include ball joints. The relationship of the relative velocities in a closed-loop mechanism is differentiated and then manipulated into set of simultaneous linear equations in the unknown relative accelerations. The derivatives of the joint-link modeling matrices, which are required to construct the vector of constants in this set of simultaneous linear equations, are formulated in terms of partial-derivative operator matrices to facilitate automatic differentiation in computer calculations. The joint-link modeling matrices, the relative velocities, and the relative accelerations are written in terms of dual numbers so to provide compact expressions which can be readily coded in object-oriented programming. The relationship of the calculated relative-acceleration components, which are expressed in the same coordinate frame, and the physical relative-acceleration components, which are naturally expressed in different coordinate frames, is developed and explained. The RSSR spatial four-bar mechanism is presented as an example of the methodology applied to a mechanism with ball joints.
ISSN:1539-7734
1539-7742
DOI:10.1080/15397734.2013.811038