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A general inversion cell, obtained from two random contra-parallelogram linkages, interconnected at the vertices of a parallelogram

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PII: 0094-114X(94)90078-7 Pergmmm Mech. Mack. Theor 7 Vol, 29. No. 6. pp. 793-801. 1994, Copyright ~ 1994 El~-vier Science Ltd Printed in Great Britain. All righB reserved 0094-114X/94 $7.00 + 0.00 A GENERAL INVERSION CELL, OBTAINED FROM TWO RANDOM CONTRA-PARALLELOGRAM LINKAGES, INTERCONNECTED AT THE VERTICES OF A PARALLELOGRAM EVERT A. DIJKSMAN Mechanism and Machine Theory, Precision Engineering. Faculty of Mechanical Engineering. Eindhoven University of Technology. Eiodhoven. The Netherlands (Received 22 March 1993. in rerised form 12 August 1993: received for publication 6 October 1993) Abstract--It is possible to interconnect two dissimilar contra-parallelgram four-bar linkages by .four turning-joints in a manner that permits (overconstrained) motion. These joints are located at the four vertices of a parallelogram. During the motion, the angles enclosed between the sides of this parallelogram do not vary. but the lengths, of which their product remains a constant, do. The overconstrained linkage mechanism, leads to the derivation of an entirely new inversion mechanism. Its inversion-cell is a 6-bar linkage of Wart's type. simply obtained from the combined linkage by erasing two interconnected bars with their turning-joints. One may show that Peaucellier's inversion-cell just appears as a very special case. INTRODUCTION There are many examples of overconstrained linkage mechanisms. One type is the one obtained by excessive interconnection of two four-bar linkages. Kempe [I] as well as Burmester [2] succeeded in doing this in different ways. Both obtained overconstrained 8-bar linkages with 2 excessive turning-joints. They took reflected- and directly similar four-bars and interconnected corresponding sides with a common turning-joint. One particular type, however, was not noticed, namely the one derived by the author at the occasion of the 7th World Congress on the Theory of Machines and Mechanisms, Sevilla in 1987 [3]. Then, the author took tw

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