Dimensional Synthesis Of Linkage Mechanism Using Feature Coupler Circles

The linkage mechanism has the advantages of compact structure,simple production,and complex and diverse output types of motion,and has broad application prospects in many fields such as medical,industrial,and aerospace.The problem of motion generation with multi-position requirements is one of the research difficulties in the scale synthesis of linkage mechanism.For this problem,scholars at home and abroad have conducted a lot of research and proposed a variety of effective methods,among which the approximate synthesis method is the most widely used.However,for more general scale synthesis problems without prescribed input angles design requirements in practical engineering applications,the existing approximate synthesis method often requires simultaneous optimization of the mechanism input angles for design requirements as a design variable with the mechanism dimensional parameters.As the number of design requirements increases,the optimization variables also increase.The effective solution of the global optimization of multidimensional variables is very difficult.Therefore,the convergence of the optimization algorithm and the stability of the design results are difficult to guarantee when using the existing approximate synthesis method to solve the scale synthesis problem of a linkage mechanism with multiple positions and without prescribed input angles design requirements.To address this problem,this paper proposes a motion generation method for four-bar mechanisms based on the feature coupler circles,which enables the solution of multi-position,without prescribed input angles design requirement motion generation problems for planar and spherical four-bar mechanisms.First,a unified mathematical model of the four-bar mechanism is established by studying the output functions of the planar and spherical four-bar rigid-body guiding mechanism at the standard mounting position.A preprocessing method for the rigid-body poses of the four-bar mechanism at the standard installation position is given.By using this method for both planar and spherical four-bar mechanisms,the shapes of the resulting attitude characteristic curves are circular arcs.Then,by analyzing the formation mechanism of the posture characteristic curve,the intrinsic connection between the corresponding circle center angle of nearby characteristic points on the feature coupler circle and the rotation angle of the mechanism linkage is discovered,and thus the method of supplementing the input angle of the rigid-body guiding mechanism in the standard installation position based on the posture characteristic curve is proposed.On this basis,the influence of the variation of the mounting parameters of the frame on the posture characteristic curve is analyzed,and the extraction method of the structural parameters of the posture characteristic curve is proposed.Thus,the input anlges supplement method is extended to the scale synthesis of the linkage mechanism in general mounting position.Secondly,the optimization objective function of the rigid-body poses input time scale is established.For the planar four-bar mechanism,the optimization variables are the2-dimensional mechanism relative input angles;for the spherical four-bar mechanism,the optimization variables are the 2-dimensional mechanism mounting angle parameters and the 2-dimensional mechanism relative input angles.Due to the low dimensionality of the optimization variables,the established optimization objective function can be used to quickly search for the approximate global optimal solution,thus achieving the input angle supplementation of the output rigid-body poses for planar and spherical quadrupole mechanisms with general mounting positions.By using the complementary input angles,the motion generation problem of the linkage mechanism without prescribed input angle can be transformed into a rigid-body guidance problem with prescribed input angles design requirements.Finally,the practicality and effectiveness of the proposed method are demonstrated by comparing arithmetic examples.Based on the theoretical study,the proposed method is used to design the guidance mechanism of human lower limb motor rehabilitation equipment.