| Mechanics & Civil Engineering |
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| A generalization of Kempe’s linkages |
| MAO De-can, LUO Yao-zhi, YOU Zhong |
| Space Structure Research Center, Zhejiang University, Hangzhou 310027, China; Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, UK |
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Abstract A new, general type of planar linkages is presented, which extends the classical linkages developed by Kempe consisting of two single-looped kinematic chains of linkages, interconnected by revolute hinges. Together with a locking device, these new linkages have only one degree of freedom (DOF), which makes them ideal for serving as deployable structures for different purposes. Here, we start with a fresh matrix method of analysis for double-loop planar linkages, using 2D transformation matrices and a new symbolic notation. Further inspection for one case of Kempe’s linkages is provided. Basing on the inspection, by means of some novel algebraic and geometric techniques, one particularly fascinating solution was found. Physical models were built to show that the derivation in this paper is valid and the new mechanisms are correct.
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Received: 19 December 2006
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