改进型Delta并联机构连续刚度映射

基于机构势能的Hessian矩阵定义机构的刚度矩阵,建立了改进型Delta并联机构的连续刚度模型.这种模型与以往刚度模型区别在于,它不仅考虑了驱动铰链、被动铰链刚度和各个部件重力对机构刚度的影响,还考虑了机构位形变化和在广义外力下各个杆件弹性变形对刚度的影响,所以该映射模型更具有一般性和精确性.最后结合刚度矩阵瑞利商定义了并联机构刚度性能判定指标λ,通过刚度性能判定指标λ在工作空间不同位置和不同受力情况下的分布,对改进型Delta机构的刚度性能进行分析和讨论.

Continuous Stiffness Mapping of Modified Delta Parallel Mechanism

The stiffness matrix of a mechanism was defined on the basis of the Hessian matrix of its potential energy, and a new continuous stiffness mapping model of the modified Delta mechanism was established. Different from the traditional models, the proposed model takes into account the influences of not only stiffness of the active/passive hinge and gravities factors on the mechanism stiffness, but also the change of the mechanism configuration and all parts elastic deformation under the constraint force. It is thus more general and exact than any other stiffness models. Finally, the characteristic index λ used to estimate the mechanism stiffness was defined by combining the Rayleigh quotient of the stiffness matrix. The stiffness characteristics were analyzed and discussed according to the distribution of stiffness index λ at both different positions in the workspace and different applied forces.