The Displacement Analysis Of Several Parallel/Serial-Parallel Mechanisms Based On Conformal Geometric Algebra

It is an important research content in the field of robotics to analyze the displacement of mechanisms with the theoretical knowledge of mechanism.Conformal geometric algebra can not only uniformly express points,lines,planes,spheres and other geometric elements,but also express the spatial motion of rigid bodies.As a new mathematical tool,conformal geometric algebra can be introduced into the study of mechanism,which can solve many difficult problems.The main content of this paper is to analyze the positive and negative position solutions in kinematics of mechanism based on conformal geometric algebra theory.The main research work is as follows:The displacement of serial mechanism is analyzed based on conformal geometric algebra.Taking FD50 N stacking robot as an example,the displacement of the serial mechanism are analyzed.In the forward displacement analysis,the corresponding spatial motion of each kinematic joint of the mechanism is directly expressed by conformal geometric algebra,and then the solution is calculated according to the given initial angle parameters.In the inverse displacement analysis,the basic geometric elements are firstly constructed by conformal geometric algebra,and then the displacement of each node of the mechanism is determined by the outer product operation.Finally,the inner product operation is used to solve the rotation angle of each joint of the mechanism,and all the inverse solutions of the position of the serial mechanism can be solved.The forward displacement of parallel mechanism is analyzed based on conformal geometric algebra.Taking the 2-RPS+SPR and 4-SPS+SPR mechanisms as examples,the forward displacement of the parallel mechanism are analyzed.In the forward displacement analysis,an unknown angle parameter is first set up,and a vertex of the moving platform is expressed according to the structural parameters and motion characteristics of the mechanism.Then the basic geometric elements are constructed by conformal geometric algebra,and the positional expression of other vertices of the moving platform are determined by the outer product operation.Finally,the initial unknown angle parameter is determined according to the dimension and geometric constraints of the mechanism.Theforward displacement of the mechanism is determined.The inverse displacement of Serial-parallel mechanism is analyzed based on conformal geometric algebra.Taking the(3-RPS)+(3-SPR),(3-RPS)+(3-SPS+UP)and2(3-SPS+UP)mechanisms as examples,the inverse displacement of the Serial-parallel mechanism are analyzed.In the inverse displacement analysis,an unknown rod length parameter is first set up,and a vertex of the intermediate platform are expressed according to the structural parameters and motion characteristics of the mechanism.Then the basic geometric elements are constructed by conformal geometric algebra,and the positional expressions of other vertices of the intermediate platform are determined by the outer product operation.Finally,the initial rod length parameter is determined according to the dimension and geometric constraints of the mechanism.Then the long input of each driving rod of the mechanism is determined,that is,the inverse displacement of the mechanism is determined.As a new mathematical tool,conformal geometric algebra has its own unique advantages in the analysis of mechanism displacement.On the one hand,the analysis process is more geometric and intuitive,on the other hand,the operation process avoids a large number of matrix operations,which makes the displacement analysis of the mechanism simpler.