# Hypocycloid degenerates to straight line

Can someone please explain if the hypocycloid described below would degenerate to a line. If possible, can someone provide an actual plot of the entire question?

The scenario is as follows:

A circle starts rolling on a flat surface. After it completes one revolution, the path starts curving up in the arc of a circle till it becomes vertical and then the path becomes vertical. During the curved part of the path, the circle performs exactly half a revolution and then completes the other half of the revolution on the vertical path. Plot the locus of the point which was initially in contact the ground.

EDIT: The problem is 2-D. Everything happens in a plane (I've copied the question exactly, except the original asks you to plot on paper). By vertical, it actually means upwards, parallel to the vertical edge of the paper and similarly for horizontal.

• What is the question you refer to? Also, this would probably be more appropriate at math.stackexchange.com – atom44 Aug 11 '16 at 9:07
• PLEASE READ THE FULL QUESTION, THE QUESTION IS WRITTEN BELOW!! Thanks for the tip anyway! – pulsejet Aug 11 '16 at 12:28
• Well @mg4w is right you do not present your problem very well. You would get a better structure for a question by presenting the things in oppsite order. Getting a good answer depends on aking a good question, unfortunately. Anyway I understand your question even in this order but i am a bit reluctant to answer the question as it basically is a request for working for free. I have no problem with answering questions of this kind its just how you put it. You dump the entire problem without any indication of even attempting to solve your problem. But I see you allready got your answer on math.SE – joojaa Aug 12 '16 at 21:02
• I have solved it on paper using constructions, but as instruments are inaccurate, I'm getting a curve in the region where the path curves up. I wanted to confirm that it is indeed a straight line, but I have no knowledge of MATLAB. Can someone at least explain how to do this sort of thing (plot or animate a point on an object moving on a path) in MATLAB, so that I can do it myself? – pulsejet Aug 13 '16 at 3:45

## 1 Answer

I discovered that this indeed hoes happen. Since radius of the path is twice of the disc, the locus is a straight line there. Used GeoGebra for the purpose! Animation