2. Loci Generated by the Point of a Line Which Moves One End on a Circle and the Other on a Line

We start from a simple geometric problem, when a straight line slides with one end on a circle and the other on a straight line (both fixed) and we look for the trajectory of a point on this straight line. We construct the equivalent mechanism which is the rod-crank mechanism, we write the relationships for the positions, we draw the mechanism in several positions and then we obtaine a succession of the curves generated by the points on this line. The case is generalized by replacing the fixed line with a mobile one, resulting a lot of curves, variable depending on the correlation of the angles of the two leading elements. The resulting curves are different from one case to another, being open curves and some having several branches [1, 2] (Luca et al. in Studies regarding of aesthetics surfaces with mechnanisms. In: Mathematical Methods for Information Science and Economics. Proceedings of the 17th WSEAS International Conference on Applied Mathematics (AMATH `12), Montreux, Switzerland, pp. 249–254, 2012; Sass et al. in J Ind Design Eng Graphics. Papers of the International Conference on Engineering Graphics and Design, Sect. 3: Engineering Computer Graphics, Nr. 12, (1):41–46, 2017).