Research On Kinematics Of Spatial 3-DOF Parallel Mechanism

Spatial three degree of freedom parallel mechanism has a wide range of applications in the field of robotics,machine tools,aerospace,mechanical processing,assembly and other industries.This article has carried on the thorough research from the following several aspects:The coupling relation of moving platform position and attitude parameter is derived from kinematic pair constraint and then independent parameters of the mechanism configuration are represented.The equivalent treatment of moving platform with tetrahedral structure to a triangle,which can decrease the number of unknowns in the equation and reduce the difficulty of position forward solution,then analytic representation of the mechanism position is gotten.According to non-independent characteristics of position of platform and attitude parameter,guidelines for determining the working space is proposed and analytic expression of working space boundary is gotten.From which the relationship between the shape,position and size of the working space and the structure parameters of the mechanism are derived.It is very useful for the synthesis and dynamic performance optimization of the mechanism.The influence of joint structure constraints on the working space is analyzed by the way of the volume of working space of spherical coordinates.The coupling relationship between the position coordinate and the attitude angle of the moving platform is obtained from the structure constraints of the mechanism.Thus an analytic expression of the workspace boundary is derived.The relative motion of a member connected by a motor can be described by motion screw.According to the property of the reverse helix,the reverse helix of the branch motion screw system is obtained,which represents the structure binding force of the branch on the moving platform.In turn,the singularity of the mechanism is transformed into the analysis of the linear correlation condition of moving platform motion screw system and the constraint screw system.Therefore the singularity of mechanism is divided into kinematics singularity and constraint singularity,The physical essence of the influence of the two kinds of singularity on the performance of the mechanism is given,and the analytical expression of the singular configuration is derived.An example is given to show the distribution characteristics of the working space and the division of the working spaceThe motion screw realized by moving platform can be analytically expressed as a linear combination of basic motion screw system.The pitch range and the axis distribution region can be used to quantify the moving range of the moving platform.The relationship between pitch and linear combination coefficient is given.They form a cubic surface.The distribution region of the axis forms a family of quadric surface.An example is given to analyze the center and the main direction of curve of twist pitch of moving platform motion screw and axis distribution surface.By transforming it into a standard form by means of coordinate translation and rotation the range of the twist pitch and the characteristic of the axial distribution surface is gotten.By establishing the simulation model of the mechanism in Pro/E and ADAMS software,the correctness of the numerical calculation is verified.The results of this paper have important value to guide the design,structure design and control of the mechanism.