An Atlas of Linkages for Independent Suspensions

Number synthesis is an important tool in mechanism design. It permits the systematic enumeration of all possible candidate mechanisms for a given application thereby placing bounds on the technology. This paper describes the application of number synthesis to the structural synthesis of independent suspensions. An independent suspension must permit vertical motions of the wheel relative to the car body, while being fairly rigid in directions orthogonal to the vertical. This is best achieved by means of in-parallel linkages, i.e., suspensions consisting of one or more chains of links and joints connected in parallel between the wheel and the car body. We enumerate all possible single-degree-of-freedom in-parallel linkages with up to five chains. A single-degree-of-freedom linkage is one in which the configuration of the entire linkage is specified by a single parameter. The discussion is restricted to linkages with revolute, prismatic, cylindric, pin-in-sphere, and spherical joints. There are 2 singlechain, 82 two-chain, 224 three-chain, 160 four-chain, and 56 five-chain in-parallel linkages which are candidates for possible use as independent suspensions. Structural graphs for all these linkages are presented. All existing independent suspensions appear in this atlas as natural products of the enumeration process.