This Demonstration gives an animation of an epitrochoid and associated planetary-motion envelope curve. The configuration shown has applications in the internal combustion engines invented by Felix Wankel and popularized by Mazda in RX-7 and RX-8 cars. The "eccentricity ratio" changes the shapes of the curves. The "reference frame" determines what is held stationary in the animation: either the epitrochoid (blue), the envelope curve (purple), or the centers of rotation of both curves. The "inner" envelope is the triangular rotor shape used in place of a piston in a Wankel rotary engine, whereas the "outer" envelope is the continuation of the envelope curve along the opposite extreme of motion.
The equations of the envelope curve are derived in the appendix of .
Some interesting extensions of this Demonstration would be to show epitrochoids and envelopes with different numbers of lobes than shown here, or to animate the Wankel engine configuration in 3D, with eccentric shaft, epicyclic gearing, or multiple offset rotors.