Methods on Mechanism Research Based on Differential Geometry
Based on the partial derivative of working space function, define the integral field of serial mechanism and parallel mechanism and serial-parallel mechanism respectively, judge conditions of singularityity including dead point and limit point with one and two and three input parameters obtained. Define the coupling degree of each input variable of mechanism use the second-order partial derivative of working space function, decoupling property between input variable identified by judging the coupling degree equal zero or not. Based on the realtionship between working space function and input variables, as well as relationship between input variables and time, three new index to weigh the kinematical properties of mechanism defined, positioning accuracy influence factor and dynamic response influence factor and sensitivity influencefactor included, its physical meaning and computation process presented as well, new direction provided for the research of kinematical properties of mechanism.
J. G. Luo and J. Y. Han, "Methods on Mechanism Research Based on Differential Geometry", Advanced Materials Research, Vols. 179-180, pp. 697-702, 2011