Mobility analysis of planar four-bar mechanisms through the parallel coordinate system |
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| Affiliation: | 1. Robotics Research Center, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China;2. Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology, Ministry of Education, Beijing Jiaotong University, Beijing 100044, China;1. Tecnológico Nacional de México, Instituto Tecnológico de La Laguna, Torreón 27000, Coahuila, Mexico;2. Universidad Autónoma de Ciudad Juárez, Instituto de Ingeniería y Tecnología, Ciudad Juárez 32310, Chihuahua, Mexico;1. School of Mechatronic Engineering, Changchun University of Technology, No. 2055, Yanan Road, Chaoyang District, Changchun City, Jilin Province, China, 130012;2. School of Mechanical Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian City, Liaoning Province, China, 116024.\n;1. Hefei University of Technology, Hefei, Anhui, PR China;2. Southwest Jiaotong University, Chengdu, PR China;3. Stony Brook University, Stony Brook, New York, USA |
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| Abstract: | This paper presents a new method for the mobility analysis of planar mechanisms. The method utilizes a geometrical representation known as “parallel coordinates.” It is a transformation that maps the Euclidean space RN to N parallel coordinates in the projective plane. Points in R2 are transformed to line segments in the parallel coordinate plane, and circles in R2 are transformed to hyperbolae. Also, in this investigation, special techniques required for mobility analysis are developed. First, the intersection of circles is performed graphically through the parallel coordinate system. The parallel coordinate plane is then appended to relate this intersection data to the angular coordinates of the various members of the linkage. The ranges of these angular coordinates are the results of the mobility analysis. |
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