欠驱动机构运动学和动力学约束不完整，机构运动具有不确定性，欠驱动机构引入柔性运动副后可利用其弹性反力一定程度上弥补动力学约束的不完整，但机构的运动学和动力学求解依然困难。针对该问题，以含有柔性移动副的平面2自由度欠驱动机构为研究对象，提出一种运动学动力学求解的数值迭代算法。在运动学、动力学建模的基础上，给定各构件的初始运动条件及原动件的运动规律，基于时间无限细分时两个时刻区间内速度和加速度不变的原理进行迭代和求解，能够得到各构件的运动规律及原动件的驱动力（力矩）。利用Matlab对该机构进行了求解，并分析了柔性移动副刚度对方程求解的影响。所提出的数值迭代算法在一定程度上突破了这类机构深入研究的瓶颈。
张建军
,
杜春翠
,
杨高炜
,
李为民
. 含柔性运动副欠驱动机构运动学和动力学求解的数值迭代算法[J]. 机械工程学报, 2018
, 54(13)
: 66
-72
.
DOI: 10.3901/JME.2018.13.066
The kinematic and dynamic constraints of under-actuated mechanism are incomplete and its movement is uncertain. The elastic reaction of flexible joints involved in an under-actuated mechanism can make up for the incompleteness of dynamic constraints in a way, but the kinematics and dynamics equations are still unsolvable. To solve this problem, a planar 2-DOF under-actuated mechanism with a flexible joint, as an example, is analyzed. A numerical iterative algorithm is proposed to solve the kinematics and dynamics. Based on the kinematics model and dynamics model, the initial conditions of all the components and the motion law of the active joint are given. In the course of numerical iteration, considered the theory that velocity and acceleration is the same in an extremely brief period, the motion laws of all the components and the driving force/torque of the active joint can be obtained. Based on Matlab programming, the kinematics and dynamics equation is solved, and the relationship between the flexible joint stiffness of the flexible joint and the driving torque is analyzed. Also, the equations solution influenced by the flexible joint stiffness is analyzed. This numerical iterative algorithm will break through the bottleneck of the further study of this kind of mechanisms to a certain extent.
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