Kinematics and Configuration Analysis of 3-PRRRR TypePure Translational Parallel Manipulator

• Main Authors: Yi-Tsung Liu, 劉乙宗
• Other Authors: Chung-Ching Lee
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/64340867573580229809

碩士 === 國立高雄應用科技大學 === 模具工程系碩士班 === 96 === This thesis focuses on the kinematics and configuration analysis of 3-PRRRR type pure translational parallel manipulator (TPM), which was proposed by Lee and Hervé [1]. Starting with the kinematic structural analysis of this kind of TPM, we define relative link-coordinate frame in each limb via Denavit & Hartenberg symbolic notations. Then, applying the 4×4 coordinate transformation technique, we derive the kinematic equations of three limbs and verify the 3-dof spatial movements with pure translation characterized by our TPM. Moreover, we further obtain the close-form solutions of inverse kinematics & numerical solutions of forward kinematics by matrix algebra and make the inverse and forward kinematic analysis in detail. Then, two numerical illustrations are provided with the help of computer-aided simulation tool, Visual Nastran 4D, and the correctness of the derived solutions is confirmed. For workspace of the manipulator, we discuss the limit ranges of three translations (PX, PY, PZ) and draw the workspace of each limb based on the forward kinematic equations. The workspace of 3-PRRRR TPM is then obtained as the intersection of the workspace volumes of three limbs. Additionally, we investigate the influence on the workspace by the variation of architecture parameters too. Finally, depending on separation of the Jacobian matrix into two matrices: one with the direct kinematics (Jx) and the other with the inverse kinematics (Jd), a general classification of singularity is introduced into three types: direct, inverse, and combined singularities. These singular configurations are also identified to avoid the postures of singularity.