If a rod of fixed length a slides with its ends on two fixed lines at right angles, its envelope is an astroid or hypocycloid of four cusps whose equation referred to the two fixed lines as axes is .

If the two lines are not at right angles but inclined at an angle 2a (a < 46°), the envelope of the rod is a curve with four eusps in shape like an astroid elongated along one of the bisectors of the axes. This curve can be shown to be an involute of the astroid.