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提出一种新型的连续型机器人动力学建模方法。首先利用NiTi合金丝超弹性的性质建立了机器人的三维实体模型,并以末端受纯弯矩为研究对象,根据欧拉—伯努利方程,得到了机器人的变形曲线方程。然后通过求解变形曲线对时间的导数,得到其上任意点的速度,进而推出连续型机器人的动能表达,再根据已有的公式导出机器人系统的势能及广义力的表达式。在此基础上,利用拉格朗日方程建立连续型机器人的动力学模型。最后通过算例仿真验证了该方法的可行性。
A new type of continuous robot dynamics modeling method is proposed. Firstly, the three-dimensional solid model of the robot was established based on the hyperelastic nature of the NiTi alloy wire. The pure bending moment at the end was taken as the research object. According to the Euler-Bernoulli equation, the robot’s deformation curve equation was obtained. Then by solving the derivative of the deformation curve over time, the velocity of the robot at any point can be obtained, then the kinetic energy of the continuous robot can be expressed, and then the potential energy and generalized force expression of the robot system can be derived according to the existing formulas. On this basis, the dynamic model of continuous robot is established by Lagrange equation. At last, the feasibility of the method is verified by a numerical example.