A new method of manufacture of hypocycloidal polygon shaft joints

The paper presents a method of machining hypocycloidal inner and outer polyhedrons on lathes and this significantly broadens the manufacturing capabilities of the latter. The method as well as the synthesis of hypocycloidal polygon shaft joints are based on a formulated and proved theorem specifying the conditions of forming a hypocycloidal n-“gon” while rotating a linear (n − 1)-gon around two parallel axes. A finite element (FE) simulation of the stressed and strained state of the synthesized hypocycloidal polygon shaft joints, affected by torque, has been performed. As a result of the numerical experiment carried out a rational variant has been selected and a convenient for engineering practice formula has been obtained, defining the carrying capacity of the synthesized polygon shaft joint.