Study On Structural Conditions And Mechanism Optimization Of 3-UPU Translational Parallel Manipulator Without The Unexpected Rotations

Because the translational parallel manipulator has the characteristics of high rigidity,high speed and high precision,this kind of mechanism has widespread application prospects in the industrial field,the Delta robot is a typical case of successful application.For the Tsai's 3-UPU parallel manipulator,the initial assembly conditions for the mechanism are given,but are difficult to achieve during the actual assembly process.In this paper,the structural conditions of the 3-UPU translational parallel manipulator without the unexpected rotations are studied,and the size parameters of the manipulator are optimized,the geometric installation modes of the outer revolute pair of the 3-UPU translational parallel manipulator are preferred.The degree of freedom of Tsai's 3-UPU parallel manipulator is analyzed,the geometric constraint equation of 3-UPU parallel manipulator is constructed.The relationship between the rank of the coefficient matrix of the geometric constraint equation of the parallel manipulator and the degree of freedom of the manipulator is discussesed.Based on this,the necessary and sufficient conditions of the 3-UPU translational parallel manipulator in theory are proved,the necessary conditions for the 3-UPU translational parallel manipulator are analyzed,the relationship between the rank of the coefficient matrix of the geometric constraint equation and the degree of freedom of the manipulator is used to solve the condition that the coefficient matrix determinant is zero when the outer revolute pairs are coplanar,the degree of freedom of the 3-UPU parallel manipulator is analyzed when the two outer revolute pairs are parallel to solve structural conditions of the 3-UPU translational parallel manipulator without the unexpected rotations.The input and output transmission indices are introduced,based on the parameter design space of the 3-UPU translational parallel manipulator,the transmission performance of the 3-UPU translational parallel manipulator is analyzed by using the global transmission index and the volume of good-transmission workspace,the performance atlases of these two optimization indices are obtained according to the defined value of the optimization index,the optimization region of the structural parameters can be obtained by means of intersection,and the optimized size parameters are selected from the optimization region,finally,the motion/force transmission performance of the 3-UPU translational parallel manipulator under the optimized size is analyzed.Based on the concept of power coefficient,the input and output constraint performance indices of the parallel manipulator are introduced,the twist screw and the constraint wrench in the UPU limb are analyzed,under the unified optimized size parameters,the constraint performance index value is calculated according to the different geometric installation mode of the outer revolute pair,the geometric installation modes of the outer revolute pair are preferred based on the constraint performance index value,and the constraint performance of the mechanism is compared and analyzed under the preferred installation modes,the constraint performance atlas when the outer revolute pairs are coplanar are drawn,the preferred region of the geometric installation mode is determined according to the performance atlas of the constraint index,an installation mode that enables the mechanism to have good constraint performance is selected from the preferred region,and the constraint performance of the 3-UPU translational parallel manipulator under the installation mode is analyzed.