By Leonard Lovering Barrett

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17 if a4 D The velocity center of the coupler of a planar four-bar linkage movement of the coupler, or the displacement analysis of a four-bar linkage. 2) The above nonlinear equation defines a relationship between ???? and ????. Singularity may appear as the binary link AB takes on different positions for four-bar linkages with different dimensions. It is a convenient way to solve the displacement equations of a planar four-bar linkage [1], which is converted into one of the two basic types of linkage by changing its fixed frame: a crank rocker for a Grashof kinematic chain and a double rocker for a non-Grashof one.

58) with a1 , ????, ????(????), and ????(????). 0499, as shown in Fig. 22. 37). Unfortunately, the intrinsic connection between the ∑ kinematics and the geometry of the movement of ∗ is not intuitively revealed in the three Planar Kinematic Differential Geometry 27 ∑ equations. In fact, the movement of ∗ is equivalent to that of the moving centrode ????m , or the ∑ moving centrode ????m rolls on the fixed centrode ????f of the fixed body without sliding, which can be viewed as the differential movement of the Frenet frame {Rf ; E1f , E2f } along the fixed centrode ????f .

78) All of these are described in the Frenet frame {Rf ; E1f , E2f }, and the same as in the Frenet frame {Rm ; E1m , E2m }, while the parameters (r, ????, ????), or (xPm , yPm , ????), are independent variables. 1 Cubic Stationary Curvature ∑ Point P of ∗ traces a path ????P in the fixed frame {Of ; if , jf }. 79) r M sin ???? N cos ???? The above relation is described in the Frenet frame {Rf ; E1f , E2f }, and may be simplified as a cubic equation in the coordinates of the moving frame {Om ; im , jm } if (r, ????) and (xPm , yPm ) are taken as independent variables for instant ????.