Research On The Principle And The Singular Configurtion Of Parallel Metamorphic Cutting Mechanism For Complex Surface

It has always been a key technical challenge to cut complex hole with large diameter on the hull surface in Chinese shipbuilding industry, which requires not only the complex motion of the torch to change the attitude and trajectory, but also the different structures to accomplish the task for the straight hole and bevel in a cycle. Thus,how to display variable configurations in the cutting process to complete the complex hole cutting more efficiently with high-quality has significant academic and application value in improving the technical level of Chinese shipbuilding industry.According to the traditional spherical joint, a novel metamorphic joint with four different configurations is introduced based on metamorphic principle, and parallel metamorphic cutting mechanism is designed with metamorphic joints. The kinematic pair screws of the source configuration branch and sub-configuration branch are analyzed based on screw theory.The DOF of moving platform is researched through screw system theory, on the basis of which the successive rotation axis of moving platform and the input selection of the mechanism are studied afterwards.The geometrical features of the source configuration and the sub-configuration of metamorphic cutting mechanism are analyzed first, and the position and attitude of the centroid coordinate system of moving platform is calculated by product of exponentials formula, after which the position constraint equations are established. Sylvester resultant elimination method is derived to simplify the constraint equations of the source configuration, and the research on the forward and inverse solution of position of the source configuration and the sub-configuration is accomplished with numerical example validated by MATLAB.The position constraint equation of metamorphic cutting mechanism is derivated with respect to time, and the Jacobi matrix is obtained. The conditions of singularity are discussed by different situations,and the relationship between the position and attitude angles is displayed, providing theoretical basis for the research on the bifurcation characteristic of metamorphic cutting mechanism afterwards.The initial motion parameters of the torch are set with respect to time,and the numerical solution of the input angles and the angular velocity is calculated through MATLAB based on the inverse position constraint equations,which is shown as curves and imported into ADAMS model as the actuator. The kinematics simulation of metamorphic cutting mechanism is finished, obtaining the relationship of the pose parameters of torch and the time,which is compared to the initial motion parameters.The relative error is in the range of 0.01,verifying the correctness of the theorical analysis method on the kinematics of metamorphic cutting mechanism. The input angular velocity curves of the source configuration are analyzed and the result shows that the motion of metamorphic cutting mechanism cannot be stable when moving close to the singular configuration.