General approach to finding the kinematic characteristics of the drives of plane mechanisms with the application of frene-serret frame and frenet formulas

Abstract

The crank pivotally linked to the mechanism link for most planar mechanisms is a driven link. The junction point of the crank and the slave link describes the circle as it is rotated. In the article, we propose to place the apex of the triangles at the point of connection. In this case, we will direct the principal normal normal to the center of the circle, and arrange the tangent tangent tangent to the circle (combine with the velocity vector of the crank). Based on this location, the crank will also rotate when rotating the crank, with the main normal being the same as the crank. The trajectories and speed of the crank in a circle will depend on the angular speed of rotation of the crank.

The basic idea of the article is to find the kinematic characteristics of the motion of the junction point of the crank and the driven link, when it makes relative motion in the coordinate system, and the moving system moves relatively stationary under a certain law. Thus the rotation of the driven link around the apex of the triangles and the movement together with it determines the motion of the driven link with respect to the fixed coordinate system.

The position of the guided link is in the projections on the triangular orths and is converted to the axis of the fixed system. In the same way, we find the absolute trajectory of movement of the point of the link, which in turn allows us to determine the speed and acceleration of the same point. The dependencies obtained are common to the driven links of the mechanism pivotally connected to the crank. For each mechanism it is only necessary to find the law of rotation of the driven link in the system of rolling triangles. We give some examples of finding the law of the rotation of the driven link for some mechanisms, as well as graphs of change of speed and acceleration of individual points of the driven link.