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并联机器人具有负载能力强、速度快和刚度大等优点,弥补了串联机器人的不足,使得并联机构成为一个潜在的高速度、高精度运动平台。针对所设计的6杆并联测量机,为解决奇异位形处的动力学性能变差和产生不可控运动等问题,基于主、被动关节所在三条支链的约束关系,推导建立了6杆并联测量机的运动学模型和闭链约束方程,将奇异性求解转化成LMI的极值问题,利用归一化GA算法仅通过15代计算实现了空间奇异位形的求解,精度达到1.168 9×10-5。所用方法避免了常规基于雅克比矩阵进行奇异性求解时产生的大量计算,具有求解精度高、收敛速度快等明显优势,为实现高速、高精度检测奠定了理论基础。
Parallel robots have the advantages of strong load capacity, fast speed and high stiffness to make up for the shortage of tandem robot, making the parallel mechanism into a potential high-speed, high-precision motion platform. In order to solve the problem of poor dynamic performance and uncontrollable movement at the singularity, a 6-bar parallel measuring machine is designed. Based on the constraint of the three branches where the primary and passive joints are located, a six-bar parallel measurement Machine kinematics model and closed-chain constraint equation, the singularity solution is transformed into the extreme value problem of LMI. The normalized GA algorithm is used to solve the singularity of space only through 15 generations of calculation, the precision reaches 1.168 9 × 10- 5. The proposed method avoids the large number of calculations that are commonly found when solving singularities based on the Jacobi matrix. It has the obvious advantages of high solution accuracy and fast convergence speed, which lays a theoretical foundation for high-speed and high-precision detection.