一种平面张拉整体机构运动学、刚度及动力学分析

Kinematics,Stiffness and Dynamics Analysis of a Type of Planar Tensegrity Mechanisms

提出了一类平面张拉整体机构的拓扑结构综合方法。设计并分析了一种由刚性杆和柔性元件联合构成的新型平面张拉整体机构,与传统并联机构相比,该机构具有质量小、惯性力小、可折叠等特点。利用绝对瞬心法解出了机构平衡状态下的位置反解,基于最小势能法对机构正解进行了分析及数值验证;对机构速度雅可比矩阵进行了推导,并对奇异位形进行了分析;通过数值计算和编程得到了机构的驱动工作空间和输出工作空间,并利用数值法验证了最小势能法和绝对瞬心法的一致性;基于能量公式对机构刚度进行了分析,并得到了机构在平衡状态下的刚度分布等高线图;采用拉格朗日方法建立了机构的动力学模型,并采用ADAMS软件对计算结果进行了验证。

A topological structure synthesis method of a class of planar tensegrity mechanisms was proposed.A new type of planar tensegrity mechanisms composed of rigid rods and flexible components was designed and analyzed.Compared with the traditional parallel mechanisms,this type of mechanisms had the characteristics of light weight,small inertia and foldable,etc.The inverse solutions of the mechanisms in equilibrium states were solved by using the absolute instantaneous center method,and the forward solutions were analyzed and numerically verified based on the minimum potential energy method.The velocity Jacobian matrix was derived,and the singular solution configurations were analyzed.Through numerical calculation and programming,the actuator workspaces and output workspaces of the mechanisms were obtained,and the numerical results by the minimum potential energy method and the absolute instantaneous center method were turned out to be identical.After that,the stiffnesses of the mechanisms were analyzed based on the energy formula,and the contour maps were obtained to reveal the stiffness distribution of the mechanisms in equilibrium states.Finally,the dynamics model of the mechanisms was established according to Lagrange method,the calculation results were confirmed by emulation in ADAMS.