具有一移动两转动并联机构设计及运动学分析

Design and Kinematics Analysis of One-translation and Two-rotation Parallel Mechanism

目的针对食品行业包装工作量大,人工成本逐级提高且易出错的现状,设计一种能实现复杂运动的新型并联机构。方法利用螺旋理论分析支链运动螺旋和约束螺旋,通过修正的Kutzbach-Grübler公式计算机构自由度。根据机构学和几何学关系,建立机构输入、输出参数关系方程;通过位置关系方程,得到机构输入、输出的速度和加速度关系方程。由于机构速度雅克比矩阵复杂,将判断矩阵是否满秩问题转化为多元函数求极值问题。根据机构约束条件,计算机构运动平台工作空间。建立机构位置正解的适应度评价函数,将改进的粒子群优化算法与迭代法相结合,求解机构位置正解。利用五次多项式对动平台中心点运动位姿进行轨迹规划,得到运动学输入参数的变化规律。结果机构具有一移动两转动自由度。通过对上述问题数学模型的求解发现,机构不存在明显奇异位形,且工作空间连续,姿态角运动范围大。求得了机构高精度位置正解,驱动副运动学参数变化平稳,符合轨迹规划预期。结论该新型并联机构满足食品抓取和装箱时所需的大工作空间要求,可以实现平稳运动,计算结果为机构动力学分析和实时控制奠定了理论基础。

The work aims to design a new parallel mechanism that can achieve complex motion in view of the status in the food industry, including large packaging workload, increasing labor cost and error-prone features. The spiral theory was used to analyze movement and constraint spirals of limb and the modified Kutzbach-Grübler formula was adopted to calculate the freedom of this mechanism. According to the relationship between mechanics and geometry, the relationship equation between the input parameters and output parameters of mechanism was built. Through the position relation equation, the relation equation of the velocity and acceleration about input and output of mechanism was obtained. Due to the complexity of the jacobian matrix, the problem of determining the matrix full rank was transformed into the problem finding the extremum of the multivariate function. According to the constraints of the mechanism, the working space of the motion platform about the mechanism was calculated. The fitness evaluation function of the positive solution of the mechanism was established and the positive position solution was solved by a method combining particle swarm optimization(pso) with iterative method. The trajectory planning of the center position about moving platform was carried out by the quintic polynomial, and the change rule of the kinematics input parameters was obtained. The results showed that this mechanism had one-translation and two-rotation degree of freedoms. By solving these mathematical models, it was found that the mechanism had no obvious singular configuration and the workspace was continuous and large. The high-precision positive position solution of the mechanism was obtained and the kinematics parameter of driving pair changed smoothly, conforming to the trajectory planning expectation. The new parallel mechanism can meet the requirement of large working space when food is grabbed and packed and realize smooth movement, and the results provide the theoretical basis for the dynamics analysis and real-time control of the mechanism.