Fourier Methods for Kinematic Synthesis of Coupled Serial Chain

Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class ofmechanisms that can be realized by coupling successive joint rotations of a serial chainlinkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits ofsingle degree-of-freedom design and control with the anthropomorphic workspace of se-rial chains. Our interest is in creating articulated manipulation-assistive aids based onthe SDCSC configuration to work passively in cooperation with the human operator or toserve as a low-cost automation solution. However, as single-degree-of-freedom systems,such SDCSC-configuration manipulators need to be designed specific to a given task. Inthis paper, we investigate the development of a synthesis scheme, leveraging tools fromFourier analysis and optimization, to permit the end-effectors of such manipulators toclosely approximate desired closed planar paths. In particular, we note that the forwardkinematics equations take the form of a finite trigonometric series in terms of the inputcrank rotations. The proposed Fourier-based synthesis method exploits this special struc-ture to achieve the combined number and dimensional synthesis of SDCSC-configurationmanipulators for closed-loop planar path-following tasks. Representative examples illus-trate the application of this method for tracing candidate square and rectangular paths.Emphasis is also placed on conversion of computational results into physically realizablemechanism designs. @DOI: 10.1115/1.1829726#

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