Stiffness Construction and Decomposition of Compliant Parallel Mechanisms

  • Chen QiuEmail author
  • Jian S. Dai
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 139)


Following the conceptual design of compliant mechanisms in Chap.  5, this chapter further looks into the stiffness properties of the developed compliant parallel mechanisms. Two types of stiffness problems are investigated, including the stiffness analysis and synthesis problem. In the stiffness analysis, the reciprocal relationship between motions and wrenches is used to design the layout of constraint limbs and construct the corresponding stiffness matrix. In the stiffness synthesis, the developed stiffness matrix is decomposed to obtain the configuration of constraint limbs based on the stiffness properties of each constraint limb. Existing synthesis algorithms are compared and categorized, including the direct-recursion and matrix-partition algorithm, and it is revealed for the first time the line-vector based matrix-partition algorithm can establish a one-to-one correspondence between the synthesized result and the initial configuration used to construct the compliant parallel mechanism. This is further verified by implementing the algorithms to decompose the constraint stiffness matrix of developed compliant parallel mechanisms.


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© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Innovation CentreNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of InformaticsKing’s College LondonLondonUK

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