Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial...Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial for linearto-rotary motion conversion.Griffis-Duffy(GD)platform is a mobile structure admitting a Bricard motion.In this paper,we present a coordinate-free approach to the design of generalized GD platforms,which consists in determining the shape and attachment of both the moving platform and the fixed base.The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints.Owing to the inversion,hidden in the geometric structure of these single-loop mechanisms,the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion,and describes the shape and attachment of the generalized GD platform.Moreover,the center of inversion not only identifies the location of rotation axis,but also affects the shape of the platform mechanism.A graphical construction of generalized GD platforms using inversion,proposed in the paper,provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.展开更多
Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in...Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in the kinematic behavior.This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator.The direct kinematic problem of the manipulator yields a quartic polynomial equation.Each root in the equation determines the assembly configuration,and four solutions are obtained for a given set of actuated joint coordinates.By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates,the direct kinematic singularity loci in the joint space are determined by the implicit function.Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve.Two assembly changing motions by encircling different cusp points are highlighted,for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos.U1813221,52075015)Personnel Startup Project of Zhejiang A&F University Scientific Research Development Foundation of China (Grant No.2024LFR015)。
文摘Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial for linearto-rotary motion conversion.Griffis-Duffy(GD)platform is a mobile structure admitting a Bricard motion.In this paper,we present a coordinate-free approach to the design of generalized GD platforms,which consists in determining the shape and attachment of both the moving platform and the fixed base.The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints.Owing to the inversion,hidden in the geometric structure of these single-loop mechanisms,the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion,and describes the shape and attachment of the generalized GD platform.Moreover,the center of inversion not only identifies the location of rotation axis,but also affects the shape of the platform mechanism.A graphical construction of generalized GD platforms using inversion,proposed in the paper,provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.U1813221 and 52075015).
文摘Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in the kinematic behavior.This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator.The direct kinematic problem of the manipulator yields a quartic polynomial equation.Each root in the equation determines the assembly configuration,and four solutions are obtained for a given set of actuated joint coordinates.By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates,the direct kinematic singularity loci in the joint space are determined by the implicit function.Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve.Two assembly changing motions by encircling different cusp points are highlighted,for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.
