On a General Method of Spatial Kinematic Synthesis by Means of a Stretch-Rotation Tensor

[+] Author and Article Information
G. N. Sandor

Machines and Structures Division, School of Engineering, Rensselaer Polytechnic Institute, Troy, N. Y.

K. E. Bisshopp

Rensselaer Polytechnic Institute, Troy, N. Y.

J. Eng. Ind 91(1), 115-121 (Feb 01, 1969) (7 pages) doi:10.1115/1.3591482 History: Received May 15, 1968


One of the key concepts in a general method of spatial kinematic synthesis is a stretch-rotation operator applied to members of a general spatial kinematic chain. The latter consists of one or more interconnected loops of successively ball-jointed bar-slideball members. Each member is represented by a vector free to stretch-rotate with the motion of the chain. In the mathematical model of the general chain, displacement is simulated by means of stretch-rotation tensors operating on each member vector. Appropriate mathematical constraints render the general chain and its mathematical model equivalent to a particular mechanism. With this approach and by taking derivatives, first, second, and higher-order loop equations can be developed which form the basis for a general method of spatial kinematic synthesis, applicable to path, function and motion generation (body guidance) with first, second, and higher-order as well as for combined “point-order” approximations.

Copyright © 1969 by ASME
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