激光聚焦次镜支撑小型三自由度机构运动分析

提出了利用一种可实现一个移动和两个转动的小型3自由度(3-DOF)并联机构来控制支撑激光聚焦次镜的方案。采用传统的欧拉角描述动平台运动方式,建立了小型3-PRS机构的运动学模型,分析了机构的正、逆运动学性能,进行了包括约束雅克比矩阵的建立和伴生运动的求解。基于运动学分析,定性分析了机构的奇异位形。联合ADAMS与MATLAB,计算了机构的可达工作空间,动平台绕x轴最大运动角度为15.167 1;绕y轴最大运动角度为13.319 4;沿z轴方向的移动大约为9.954 1 mm,分析证明该小型3-PRS机构完全满足支撑激光聚焦次镜结构的设计要求。

Kinematic analysis of a 3-DOF mini mechanism based on laser beam focusing by bracing the secondary mirror

A 3-DOF parallel 3-PRS mechanism, which can realize one translational and two rotational motions and also can brace the secondary mirror used in laser beam focusing, was proposed. Traditional Euler angle for describing the motion of moving platform was adopted, and based on that, kinematic model of a 3-DOF mini mechanism was built to analyze its direct and inverse kinematics performances including Jacobian matrix generation and solving the problem of accompanying motions. Furthermore, qualitative analysis of singularity and quantitative analysis of the reachable workspace of the mechanism were given. By combining ADAMS with MATLAB, the maximum and minimum motions of the moving platform including the motions of rotational x axis, rotational y axis and along z axis were approximate 15.167 1, 13.319 4 and 9.954 1 mm respectively. The derived results strongly prove that a 3-DOF mini mechanism can fulfill the design requirement of the supporting structure of supporting the secondary mirror using laser beam focusing.