TY - CHAP

T1 - Stiffness Construction and Decomposition of Compliant Parallel Mechanisms

AU - Qiu, Chen

AU - Dai, Jian S.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85087548057&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-48313-5_6

DO - 10.1007/978-3-030-48313-5_6

M3 - Chapter

AN - SCOPUS:85087548057

T3 - Springer Tracts in Advanced Robotics

SP - 81

EP - 98

BT - Springer Tracts in Advanced Robotics

PB - SPRINGER

ER -