Jacobian analysis for lower mobility parallel robots based on actuating wrenches

The lower mobility parallel robots have been applied in lots of industrial fields, and the Jacobian plays an important role in the robotic performance analysis such as velocity analysis, precision analysis, and stiffness analysis. As for lower mobility parallel robots with the special limb structures, a novel approach based on actuating wrenches is proposed for the Jacobian analysis, which is much concise compared with the existing methods and significant for the proposed physical concept of the actuating wrench. The characteristics of the special limb structures are explored, and these structures are frequently adopted to constitute the lower mobility parallel robots that are extensively utilized in industry. The Jacobian matrix is derived just through the actuating wrenches. Not only the velocity Jacobian but also the force Jacobian is analyzed, and some incorrect deduction between the two Jacobian matrices appeared in the published works is clarified. Examples show that if the origin of the global coordinate frame is set at the moving platform, the Jacobian analysis can be much simplified.