Dynamic modeling and analysis of 3-RRS parallel manipulator with flexible links

Abstract

The dynamic modeling and solution of the 3-RRS spatial parallel manipulators with flexible links were investigated. Firstly, a new model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Secondly, according to the kinematic coupling relationship between the moving platform and flexible links, the kinematic constraints of the flexible parallel manipulator were proposed. Thirdly, using the kinematic constraint equations and dynamic model of the moving platform, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. Furthermore, a few commonly used effective solutions of second-order differential equation system with variable coefficients were discussed. Newmark numerical method was used to solve the dynamic equations of the flexible parallel manipulator. Finally, the dynamic responses of the moving platform and driving torques of the 3-RRS parallel mechanism with flexible links were analyzed through numerical simulation. The results provide important information for analysis of dynamic performance, dynamics optimization design, dynamic simulation and control of the 3-RRS flexible parallel manipulator.

Dynamic model and input shaping control of a flexible link parallel manipulator considering the exact boundary conditions

“…Substituting Eqs. (15) and (16) into Eqs. (10)- (12), algebraic manipulation yields the following nonlinear coupled dynamic equations:…”

“…Yu et al 15 developed a dynamic model of a 3-RRR robot with elastic linkages, and experiments were carried out to verify the effectiveness of the model presented. Liu et al 16 investigated a dynamic model of a 3-RRS flexible robot with a parallel structure based on a spatial element model of elastic links. Using AMM, Zhang et al 17 presented a dynamic model of a PPM focused on the one-way modeling method.…”

Dynamic Analysis of Flexible-Link Planar Parallel Manipulator with Platform Rigidity Considerations

“…Shan-Zeng [21] derived the dynamic modeling equations of a 3-RRS manipulator with flexible links, analyzed the dynamic response of the end-effector, and indentified the actuator torques required to drive the flexible mechanism. Vakil et al [22] introduced a method by combining the assumed mode shape approach and Lagrange's equations to obtain a closed-form finite dimensional dynamic model for planar flexible-link, flexible-joint manipulators. Reis and Sada Costa [23] proposed a linear quadratic regulator theory for trajectory control of single link flexible arm.…”

Determining workspace parameters for a new type of 6RSS parallel manipulator based on structural and geometric models

“…Regardless of the number of degrees of freedom, fewer [1][2][3][4][5][6][7][8] or more [9][10][11][12], the parallel mechanisms have proven their utility in various domains such as flight simulators, telescope position control, radar antennas, pointing devices [13].Parallel mechanisms have a robust construction and can move bodies of considerable mass and size at high speed, establishing a translational motion or rotation of the mobile platform. Compared to serial mechanisms, parallel manipulators have some special characteristics: high rigidity, high dynamic loading capacity, chain closed structure, high positional accuracy.…”