Quinquinomial Power Laws of Motion of Cam Mechanisms

摘要

The quinquinomial power laws of motion make it possible to modeling laws of motion without finite and infinite spikes that result in better dynamic characteristics of high-speed, elastically deformable cam-lever systems compared to other laws of motion. Therefore, after applying a rational possibility for generating quinquinomial power laws of motion suitable for synthesizing polydyne cam mechanisms, a family of these laws has been studied. The derived family of normalized quinquinomial power functions makes it possible to compile laws of motion without a finite and infinite spikes of cam mechanisms with better dynamic characteristics compared to trinomial and quadrinomial power laws of motion in the synthesis of high-speed, flexible cam-lever systems. This is because the parameters of the functions are derived from the condition for zeroing the first four derivatives of the normalized function at the beginning and at the end of the output move. At low speeds, the real and the basic function of the output displacement practically coincide. At high values of speed, load, elastic deformations, and gaps of the cam-lever systems, a small part of the stroke of the executive link is lost. It is possible to preserve the type of the basic law of motion by slightly increasing the basic stroke of the output unit so as to compensate for the reduction in the travel (stroke) of the executive link.