Type Synthesis Of Parallel Mechanisms With A Constant Jacobian Matrix

The Jacobian matrix of parallel mechanism is defined as the map of the velocity and force of the end-effector into the vector of actuated joint rates.It is foundation of performance analysis and evaluation for parallel mechanism.In general,for the majority of parallel mechanisms,their Jacobian matrices are variables with different poses in workspace.Lots of motion and force performance parameters would change as well.Assume that the matrix keeps constant in any poses.Then,most of performance indices are invariant.Thus,it will bring a great deal of convenience for mechanism to analyze and design,thus having great importance to improve the control accuracy of parallel mechanisms.Based on this,the parallel mechanism with the characteristic of the constant Jacobian matrix is discussed,and an approach for the synthesis of parallel mechanisms with a constant Jacobian matrix is then proposed.The main research contents are as follows:Firstly,based that the constant transmission screw and the reciprocal product between the transmission screw and the main twist screw is constant,the relationship between the main twist screw and the constant transmission screw is discussed.Then the criteria for constant matrix of translational,rotational and mixed-motion parallel mechanism are proposed after a classification of rotational and mixed-motion parallel mechanism based on the transmission screw and mobility property of the moving platform.Secondly,the type synthesis principle of the parallel mechanism with the constant Jacobian matrix is introduced.Using the principle,parallel mechanisms with a constant Jacobian matrix are synthesized in two steps: the configuration design and the combination of the limbs.Then,based on the constraint screw theory and the criteria of the parallel mechanisms with a constant matrix,the limbs with 5,4,3 and 2 DoFs which meet the criteria of the constant Jacobian are synthesized systematically.When the constraint of the limbs satisfies the corresponding geometrical arrangement and the reasonable actuated joints are guaranteed,the parallel mechanisms with a constant Jacobian matrix are obtained.In addition,the reason that the Jacobian matrices of the ? type and the ? type of rotational parallel mechanisms do not keep constant and the conclusion that for the ? type of rotational parallel mechanisms and the ? type of mixed-motion parallel mechanisms must be isotropic parallel mechanisms once their Jacobian matrices are constant are confirmed.Finally,several cases of the partial invariance of the Jacobian matrix are discussed.The limb combination of the parallel mechanisms with partial invariance of the Jacobian matrix is explored.Through analyzing velocity of the translational PPRR-CRR-CPR parallel mechanism and mixed-motion 3-PPR parallel mechanism,the results demonstrate correctness of the theory.