Rational possibility of generating power laws in the synthesis of cam mechanisms

Introduction.The generation of polynomial power laws of motion for the synthesis of cam mechanisms is complicated by the need to determine the coefficients of power polynomials. The study objective is to discover a rational capability of generating power law swith arbitrary terms number under s with an rbitrary number of terms under the synthesis of cam mechanisms.Materials and Methods.A unified formula for determining the values of coefficients of power polynomials with any number of integers and/or non-integer exponents is derived through the so-called transfinite mathematical induction. Results.A unified formula for determining the values of coefficients, which gives correct results for any number of even and/or odd exponents, is presented. The correctness of the derived formula is validated by the results on the multiple checks for different numbers, even and odd values of the exponents of quinquinomial and hexanomial power functions. Discussion and Conclusions. A unified formula for determining the values of coefficients of power polynomials makes it possible to rationally define the laws of motion without finite and infinite spikes in the synthesis of elastic cam-lever systems. This provides a rational determination of the laws of motion without finite and infinite spikes in the synthesis of elastic cam-lever systems, and simple verification of the accuracy of the results obtained. The functions are particularly suitable for the synthesis of polydyne cams, as well as cams, since one polynomial can be used throughout the entire geometric mechanism cycle.