### Discussion: "Mechanical Couplings—A Geometrical Theory" (Fichter, E. F., and Hunt, K. H., 1977, ASME J. Eng. Ind., 99, pp. 77–87)

E. J. F. Primrose
1977 Journal of Engineering for Industry
quite different from a rigid pendulum which "plows" into an inclined surface while maintaining its circular path. When a revolute pin impacts against a normal surface which has a lateral velocity, the friction force causes the pin to rebound obliquely. A rigid pendulum, on the other hand, is constrained and must rebound normally. Assuming that its contact zone is symmetrical about a tangential plane, the pendulum would neither lose nor gain energy since the resultant friction force travels
more » ... gh no distance and hence does no work on the pendulum. I Mechanical Couplings-A Geometrical Theory 1 E. J. F. Primrose. 2 The authors have presented a most interesting paper, which uses purely geometrical arguments to throw light on the behaviour of mechanical couplings. However, in my opinion, they go too far in stating their Theorems 1 and 2, which I believe are untrue in their present form. A critical example is that of the elliptic trammel and its generalization, the spatial PSSP, which the authors discuss in Part 2. Taking the spatial PSSP, the degree of the ruled surface Y, generated by the SS line is 4, and the order of the curve r (an ellipse) described by a point Q on the SS line is 2, as the authors say. This would, of course, disprove Theorem 1, but the authors claim that the order of r is really 4, on the grounds that the plane of r meets X! in a curve of order 4, consisting of r and the line at infinity counted twice. This is perfectly true, but I maintain that the line at infinity is not part of the locus of Q. It arises because there are two (imaginary) positions of the linkage in which the SS line is at infinity (this can be established by setting up a suitable coordinate system). In each of these two positions, the point Q is at infinity, of course, and these two positions of Q are the (imaginary) points at infinity on the ellipse r. There is, therefore, an essential difference between the degree of the surface £ and the order of the curve r, which disproves Theorem 1. Theorem 2 now falls to the ground because "feather" is no longer an invariant property of a connectivity-1 algebraic coupling.