Lagrange equations of nonholonomic systems with fractional derivatives

This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton＇s principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d＇Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d＇Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d＇Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.

立体料仓预设防撞点后的6R机器人运动分析

针对6R关节型机器人在上/下料过程中与矩阵式立体料仓存在的偶发性碰撞问题,对6R关节型机器人与矩阵式料仓交互运动过程进行建模,在立体料仓前添设矩阵式防撞点,分析6R关节型机器人的姿态及运动。基于标准D-H法和Robot Toolbox平台对研究模型做正逆运动学仿真来验证正确性;基于拉格朗日方程建立动力学模型,验证机器人末端操作器在矩阵式立体料仓的随机坐标点处连续运动的位姿正确性,求解连续过程中有/无防撞点的力矩随时间变化的动态性能,对比分析仿真结果。仿真结果表明:采用本文方法可使机器人运动精度达到0.039 mm,运行平稳。