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Stiffness Construction and Decomposition of Compliant Parallel Mechanisms

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Analysis and Synthesis of Compliant Parallel Mechanisms—Screw Theory Approach

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 139))

Abstract

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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Authors and Affiliations

  1. Innovation Centre, Nanyang Technological University, Singapore, Singapore

    Chen Qiu

  2. Department of Informatics, King’s College London, London, UK

    Jian S. Dai

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  1. Chen Qiu
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  2. Jian S. Dai
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Correspondence to Chen Qiu .

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Qiu, C., Dai, J.S. (2021). Stiffness Construction and Decomposition of Compliant Parallel Mechanisms. In: Analysis and Synthesis of Compliant Parallel Mechanisms—Screw Theory Approach. Springer Tracts in Advanced Robotics, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-48313-5_6

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