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：Aiming at the heavy-load parallel robotic manipulators, other than classic sequential 'topology-dimension-structure' parameter design methodology, this paper proposes a new way to optimize dimension and structure parameters 2 simultaneously. To deal with the low-speed but heavy load working environment, a new type of stiffness performance evaluation index is introduced based on kineto-elastic statics (KES) analysis. This stiffness distribution index, mainly focuses on the stiffness distribution among all parts in the manipulator, along with two other dynamic performance indices and some dimensional constraints, formulate a multi-objective optimization model.Then the particle swarm optimization (PSO) algorithm is introduced to search for the optimum parameters. This method is applied on a widely used TRICEPT parallel manipulator, the dynamic performances before and after optimization are compared to verify this effectiveness of this method.

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This paper presents an alternative decomposition of spatial stiffness matrices based on the concept of compliant axes. According to the congruence transformation of spatial stiffness, the coordinate-invariant aspects, which are referred to as the central principal components of the 6 × 6 symmetric positive semidefinite matrices, can be derived uniquely. The proposed decomposition is free from the eigenvalue problems of the 6 × 6 stiffness matrices so that both Plücker's ray and axis coordinates can be utilized to characterize the elastic system's force-deflection behavior. Hence, an arbitrary spatial stiffness matrix can be uniquely decomposed into two sets of orthogonal spring wrenches with finite and infinite pitches, respectively. The decomposed wrenches with finite pitches correspond to the stiffness' wrench-compliant axes, along which linear deformations produce only wrenches parallel to them. As a result, three torsional and three screw springs are required, at the most, to realize a given spatial stiffness. Using the principal axes decomposition, some physical appreciations, such as the center of stiffness, the wrench-compliant axes, and the correspondence of compliance and stiffness, can be derived to reveal the inherent structure of spatial stiffness in an intuitive manner. In order to verify the effectiveness of the proposed method, two numerical examples are intensively studied with comparison to the eigenscrew decomposition. In addition, a potential application of the proposed stiffness decomposition method is also provided for the structural compliance modeling of flexible links in robot manipulators.Index Terms-Center of stiffness/compliance, force-deflection behavior, spatial stiffness matrix, wrench-compliant axis.