Study On Lower-mobility Parallel Mechanisms With Axis Errors

The kinematic properties of the lower-mobility parallel mechanisms are determined by the arrangement of the limbs and the axis directions of the joints in the limbs.Due to the existence of machining and assembly errors,the axis directions of the joints always deviate from where they should have be,which will affect the constraint properties of the limb and make the parallel mechanism have uncontrollable degrees of freedom.This phenomenon is particularly evident in the parallel mechanism composed of the UPU limb.Taking 4-UPU parallel mechanism as example,it can produce undesired rotation around X axis and Y axis under external force when the input joints are locked.From the analysis of the causes of this kind of phenomenon,a series of lower-mobility parallel mechanisms with stable constraint properties are studied and synthesized to avoid the emergence of uncontrollable freedom.1.From the point of view of limb constraint,the influence of geometrical relation errors on the properties of limb constraint of parallel mechanism is analyzed.The results show that different geometric axis errors have different effects on the limbs with different constraint properties.For the constrained couple limb,the axis error of the moving pair does not affect its constraint properties.For mixed constrained limb,the constraint properties of the limb will be changed as long as the axis error occurs.Therefore,the mixed constraint limb which is insensitive to error is nonexistent.2.The uncontrollable degree of freedom of the mechanism is measured by judging whether the overall Jacobian matrix is full rank.Taking 4-UPU parallel mechanism as an example,the possible axis errors can be divided into four categories.Based on the screw theory,the root cause of the uncontrollable degree of freedom on the moving platform of the mechanism is explained.Combined with Solid Works and Adams simulation,the 4-UPU uncontrollable degree of freedom phenomenon is verified3.In order to avoid the descending rank of the overall Jacobian matrix,a configuration synthesis method of parallel mechanisms with stable constraint property was proposed.Through stable constraint limb synthesis,a series of limb with stable properties can be obtained,which can avoid the constraint singularity caused by the change of limb properties.Through drive synthesis,a reasonable drive arrangement scheme is proposed for different limb,which can avoid the drive singularity or platform singularity of the parallel mechanism.Finally,a kinds of lower-mobility parallel mechanisms with stable constraint property are synthesized.4.Taking the integrated 3T1 R parallel mechanisms 3-CPS+PCP as example,it is verified that the axis error would not lead to the occurrence of uncontrollable degree of freedom through the simulation.In order to analyze and compare the influence of different errors on the output precision of the mechanism,the kinematics error model of the mechanism is established based on vector method.According to sensitivity analysis,the sensitivity of each error source is obtained.The tolerance range of each error source under certain output error condition is given by using the 3σ criterion.Finally,the output error of the 3-CPS+PCP mechanism is limited to a certain range by precision design.The effectiveness of the precision design is verified by using the Monte-Carlo method to estimate the accuracy.