Abstract
This paper presents an approach for the structural synthesis of kinematic chains with multiple joints based on the concept of contracted graphs. A graph representation of multiple joints is introduced and the modified Euler formula is derived. Then, contracted graphs of kinematic chains with m multiple joints and L ind independent loops are synthesized from the catalogs of contracted graphs of kinematic chains with simple joints and L ind + m independent loops. Finally, basic kinematic chains with multiple joints are obtained from their corresponding contracted graphs. As a result, the number of kinematic chains with one and two multiple joints up to ten links are listed.
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