Kinematic equations that express the position and the orientation of the platform as functions of actuated joint displacements are commonly used to develop the workspace of 6-DOF parallel manipulators. For 3-DOF parallel manipulators with RPS or PRS chains, it is much easier to develop kinematic equations that relate passive joint displacements to the actuated joint displacements. The existing methods provide actuated joint displacements to solve for the passive joint displacements that are then used to develop the workspace. This approach cannot directly obtain the boundary, investigate the shape, or evaluate the volume of the workspace. This thesis presents methods to develop the compatible reachable workspaces (defined as the set of all attainable positions that can be reached through a continuous motion starting from the initial assembly configuration) of 3-DOF parallel manipulators with RPS or PRS chains. The proposed methods can directly obtain the workspace boundary, and the shape and the volume of the workspace can be determined using the cross-sections of the workspace. The workspace boundary consists of many 2-DOF patches generated by different sets of equations. Some related rules are proposed to facilitate the searching process for the correct equations. The effects of passive joint limits and dexterity measures on the workspace are studied. The kinematics and instantaneous kinematics of the manipulators are also investigated.
Keywords: 3-DOF parallel manipulators; reachable workspace; kinematics; 3-RPS; 3-PRS.

Kinematic equations that express the position and the orientation of the platform as functions of actuated joint displacements are commonly used to develop the workspace of 6-DOF parallel manipulators. For 3-DOF parallel manipulators with RPS or PRS chains, it is much easier to develop kinematic equations that relate passive joint displacements to the actuated joint displacements. The existing methods provide actuated joint displacements to solve for the passive joint displacements that are then used to develop the workspace. This approach cannot directly obtain the boundary, investigate the shape, or evaluate the volume of the workspace. This thesis presents methods to develop the compatible reachable workspaces (defined as the set of all attainable positions that can be reached through a continuous motion starting from the initial assembly configuration) of 3-DOF parallel manipulators with RPS or PRS chains. The proposed methods can directly obtain the workspace boundary, and the shape and the volume of the workspace can be determined using the cross-sections of the workspace. The workspace boundary consists of many 2-DOF patches generated by different sets of equations. Some related rules are proposed to facilitate the searching process for the correct equations. The effects of passive joint limits and dexterity measures on the workspace are studied. The kinematics and instantaneous kinematics of the manipulators are also investigated.
Keywords: 3-DOF parallel manipulators; reachable workspace; kinematics; 3-RPS; 3-PRS.

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