On the Bennett Mechanism

Abstract

Bennett chain is an exceptional chain having four turning pairs whose axes of rotation are neither parallel nor concurrent. To speak generally, such disposition of the axes is known to produce a four-link chain which is completely stiff, and so furnishes no kinematic chain at all. Now it is questionable whether there is any other such skew kinematic four-link chain than the Bennett chain or not, so this questionable point is studied and the following result is obtained : If a skew four-link mechanism which has four turning pairs and four central axes forming a skew quadrilateral has one degree of freedom, it must be the Bennett Mechanism. Next, it is pointed out that the relationship between input and output angles in the Bennett mechanism coincides with the one in the elliptic gears. This simple remark may give us a useful application of the Bennett mechanism.