Design And Analysis Of Spherically Redundant Mechanism For Flight Simulator

3-RRR spherical parallel manipulator has three rotational degree-of-freedom and all joints are revolute pairs.It can be used as a flight simulator.But the stiffness of the link-ages is low in the 3-RRR spherical parallel manipulator and it belongs to over-constraint parallel manipulator.Redundant actuation is a good method to improve the stiffness of the linkages.3-RRS spherical parallel manipulator is not over-constraint parallel manipu-lator to substitute the 3-RRR manipulator as a flight simulator.The whole paper includes the analysis of the degree-of-freedom,kinematics,capability and dynamics.Three kinds of redundant actuation parallel manipulator are proposed,including 4-RRR redundant actuation parallel manipulator,3-RRR redundant actuation parallel ma-nipulator with spherical parallelogram,double 3-RRS spherical parallel manipulator and a hybrid manipulator based on double 3-RRS spherical parallel manipulator.Screw theory is used in the analysis of the degree-of-freedom.It redefines the num-ber of order in the mathematics and proves that the number of order may not be three,but six.The hybrid manipulator's degree-of-freedom is obtained by the means of the computation and the logical judge.There are three rotational degree-of-freedom and a redundant degree-of-freedom in the hybrid manipulator.Spherically analytical theory is used in the analysis of the kinematics,instead of traditional method of vector-rotation.Direction-cosines are given out by spherically an-alytical theory.Principle of the constant angle is used to build the constraint equations.A numerically forward algorithm is used in the process of the analysis of the kinematics.The numerical algorithm is similar to Newton-Raphson method and is based on Jacobian and inverse kinematics,which is not based on the constraint equations.Conditioning number of the Jacobian is used to analyze the capability of the manipu-lator.The capability includes the stiffness,dexterity,torque and singularity.The equation of the stiffness is simplified,not considering the material's stiffness,just Jacobian matrix included.It makes the computation simple.A relationship is found between the dexterity and the workspace that explains the practical meaning about the dexterity.Lagrange equation is used in the process of the dynamical analysis.In general,the solutions are not unique about the input forces in the redundant actuation parallel manipulator.In this paper,a simple method is presented to analyze the dynamics of the 3-RRR spherical parallel manipulator with parallelogram.Double 3-RRS parallel manipulator are divided into two 3-RRS parallel manipulator to analyze the dynamics and the method avoids complicated algorithm in mathematics.