Study On Invariants And Accuracy Of Discrete Motion Of R-pairs

In this dissertation,the kinematic geometry of the rigid body motion is developed to the rotational error motion.The global geometrical properties of the rotational error motion are studied using the invariants and invariant equations of the rigid body motion.The invariant accuracy of the actual revolute pair is defined,and its test,analysis and evaluation methods are discussed;furthermore,the identification and compensation methods for invariant errors are studied.(1)The sufficient and necessary conditions for a general rigid body motion degrades into cylindrical motion,helical motion and rotational motion are presented and proved.Based on the kinematic geometry,the kinematic properties of the motion constrained by C-pair,H-pair and R-pair,and the local and global geometrical properties of the line-trajectories are studied.The invariants and invariant equations of the three kinds of motions are deduced,while the sufficient and necessary relationships between the invariants and the constraints of the three kinds of kinematic pairs are proved.(2)The global geometrical properties of the discrete line-trajectories traced by the lines in rotational error motion are studied.The invariants of the rotational error motion,including the minimal spherical image curve and the minimal striction curve,are deduced and used to describe the deviations between the rotational error motion and the ideal motion.Based on the invariants,the geometrical properties of the discrete trajectories,traced by different points,lines,planes and cylinders in rotational error motion,are studied,which provide the basis for accuracy test and analysis of R-pairs.(3)The conception of invariant accuracy for the rotational error motion are presented,which makes the accuracy indexes of revolute pairs unrelated to the measuring positions and revolutions.The kinematic geometrical model for testing revolute pair’s errors with a double ball artifact is set up,and the six kinematic parameters of the error motion are calculated using the data measured.The invariants of rotational error motion are divided into the translational errors and angular errors.The changes of the invariant errors in different revolutions and the convergences of the invariant errors as the total number of revolutions increase are studied.(4)A mechanism model with redundant and elastic constraints is presented to describe the invariant accuracy characteristics of the R-pair.The redundant and elastic constraints of the actual R-pairs are discussed,and the geometrical and physical equations of the mechanism model are studied.The relationships between the invariant accuracy and its influence factors,such as the structures,the geometrical parameters and their errors,the physical properties of the components and the loads,are established.This mechanism model realizes the accuracy analysis of the revolute pair with its kinematic and dynamic solutions.(5)The moving axis of an R-pair is defined using the minimal spherical image curve and the minimal striction curve,while the fixed axis of an R-pair is defined as the geometric axis the trajectory traced by the moving axis.The kinematic pair errors and the link errors of the actual kinematic chain are distinguished using the moving and fixed axes.Based on these definitions,the mechanism models of the rotary table in a 5-axis machine tool and a SCARA robot are set up.Some new methods for error test,analysis,identification and compensation of the actual kinematic chain are developed.