tailieunhanh - Advances in Robot Kinematics - Jadran Lenarcic and Bernard Roth (Eds) Part 10

Tham khảo tài liệu 'advances in robot kinematics - jadran lenarcic and bernard roth (eds) part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 266 P. Ben-Horin and M. Shoham determinant he found two conditions one constituting a linear complex and the second constituting a linear congruence of the lines along the manipulator extensible links. The same result was also obtained by Di Gregorio 2002 who used mixed products of vectors identified in the robot to obtain the singularity condition as a ninth-degree polynomial equation. Another decoupled robot whose singularity was found is the 3-2-1 structure. Using an ellipsoidal uncertainty model for a 3-2-1 wirebased system Thomas et al. 2002 found that the singularity of this robot occurs when one of three tetrahedrons constituted by the joints is singular. The same result was obtained by Downing et al. 2002 who approached the problem by using the pure condition proposed by White 1983 also used in the present paper . The results of Thomas et al. and Downing et al. go along with the comments of Hunt and Primrose 1993 regarding the singularity of the 3-2-1 structure. The approach used in this paper is based on Grassmann-Cayley algebra. The origin of this algebra date back to Grassmann treatise Theory of extension in 1844. The basic elements of this algebra are geometric entities such as points lines and planes and the basic operators are able to express algebraically the intersection meet or the union join of two or more elements. A complete definition of the meet operation came out after more than a century in the paper of Doubilet et al. 1974 . In the present investigation we provide a comprehensive study of the singularity conditions of a class of 18 robots that have three concurrent links on the moving not generally planar platform. This is a continuation of previous studies on the singularity of a class of seven GSPs having only pairs of concurrent joints Ben-Horin and Shoham 2005a and a broad class of three-legged robots Ben-Horin and Shoham 2005b . The main aim of this paper is to demonstrate the simplicity of the use of Grassmann-Cayley algebra for .

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