综合关节和杆件柔性的机械臂刚柔耦合建模与仿真

基于Lagrangian方程和转子非线性扭簧模型,建立柔性机械臂刚柔耦合动力学模型;通过假设模态法将物理坐标转换为模态坐标;利用ADAMS建立了虚拟样机,用于求解仅考虑杆件柔性时的运动;在Matlab中编写了Runge-Kutta算法,用于求解综合关节和杆件柔性时的运动。针对重力和驱动力作用下的垂直面摆动,给出了不同末端负载影响下的柔性关节转角和末端变形曲线;分析了关节柔性与杆件柔性之间的耦合关系。结果表明关节柔性不可忽略,关节和杆件柔性耦合作用下的末端振动小于两者的叠加,振型由关节和杆件的柔性确定,但幅值主要受驱动力影响。

Dynamics and Simulation of Rigid-flexible Coupling Robot Arm with Flexible Joint and Link

For the flexible manipulator, rigid-flexible coupling dynamics model was established based on the Lagrangian equations by regarding the flexible joint as a non-linear torsional spring model. Assumed model method was used to transform physical coordinate to modal coordinate. ADAMS was adopted to build virtual prototype for simulation of link flexibility. A Runge-Kutta algorithm was programmed by Matlab to solve dynamics equations considering both link and joint flexibility. Aiming at simulation of manipulators swing under the gravity and driving torque, tip deformation and angle under different loads were given. Coupling characteristics of the joint and link flexibility were studied. Results showed that joint flexibility could not be ignored. The vibration range of manipulator under coupling of the joint and link flexibility was less than sum of individual flexibility vibration. Vibration mode was determined by the joint and link flexibility jointly, but amplitude was mainly influenced by driving torque. The dynamics and solving method were proper.