共轴球面并联跟踪机构运动学建模与应用

打开文本图片集

Kinematic modeling and application of coaxial spherical parallel trackingmechanism

* Corresponding author， E-mail：zhumingchao@ciomp. ac. cn;dengyongting@ciomp. ac. cn

Abstract： To address the requirements of dynamic tracking tasks demanding extensive motion range，high stifness，and rapid response，this study examines a coaxial 3-RRR spherical paralll mechanism for optical dynamic tracking applications. Initially，the mechanism's forward and inverse kinematics are analyzed using a geometric vector method. Vector projection is employed to identify the unique inverse kinematic solution corresponding to the actual configuration from eight analytical candidates. Subsequently，a singular forward kinematic solution is determined from up to eight closed-form solutions by applying the proposed inverse kinematics algorithm.Furthermore，integrating the forward and inverse kinematic algorithms with a motion singularity index and a colision avoidance strategy，the reachable Cartesian and configuration spaces are systematically characterized under singularity-free and collision-free conditions.A unit quaternion-based spherical interpolation method is introduced to guarantee smooth orientation transitions of the moving platform within the workspace. Both computational and experimental results demonstrate that the analytical forward kinematics solution enhances computation speed by 94% compared to conventional constraint-based iterative methods，while reducing numerical error to the order of 10-14 and obviating the need for initial value estimates.Workspace analysis reveals that the mechanism achieves a pitch range from （204号 48.42∘ to 138.42∘ and a full azimuthal range of -180∘ to 180∘ ，maintaining the rolling degree of freedom about the pointing axis within this domain.Theoretical and experimental findings confirm that the pro posed coaxial spherical parallel tracking mechanism exhibits superior motion performance，fully meeting the demands of optical dynamic tracking applications.

Key words： parallel mechanism；dynamic tracking；forward and inverse kinematics；workspace； trajec tory planning；coaxial spherical

1引言

传统的光电经纬仪跟踪架机械惯性较大，响应速度相对较慢，无法进行连续大仰角运动，存在过顶死角。（剩余14809字）