Cycloidal motion generation leads to gearing (with matlab code)
Figure 1: Two link system
These equations, (1) and (2), are parametric equation of a hypo-cycliod curve. This means to generate a constant gearing in reverse direction, the endpoint must trace a hypo-cycloid curve. The curve generation is visualized in in the video linked on the left. The codes can be found through the button below.
In this section , we discuss the generic solution with the two link model and show that epicyclic gear train's design uses the gearing based on this principle.
Figure 3: Epicyclic gearing expressed as 2 bar linkage system.