If the arms are fixed at a right angle
Notes: 1) The solution is my own (Geogebra practically solves it for you). 2) The positions of A, B, C are given by moving the red point. This point is not part of the solution, which means this construction goes backward. To solve the problem, I went in this order: Draw the axes of the two arms. Let A move freely on the first arm. Choose a means of fixing the segment length AB. Construct AB. B is dragged along the second arm as A moves. Determine the ranges of A and B on the two arms. Construct arbitrary C, rigidly connected to A and B. The solution must be an ellipse. There is no other possibility. Locus[] confirms the suspicion. Now, when A reaches either end of the arm, what direction will the triangle rotate? It depends on the motion of the system, and its arrangement in space. We could also choose a direction of rotation by applying force to B or C when A reaches the end of an arm. Or by any number of mechanical means. So, one option is to introduce mechanics. I think that is a beautiful choice.* Another, more convenient alternative is to rotate the triangle with a dial. :) *Like this: [url]http://www.geogebratube.org/material/show/id/71230[/url]