The Closed Differential Pulley: Analysis of Its Rotational and Linear Motions

A mechanical system of special design, primarily for instructional purposes, is proposed, mathematically analyzed, and tested experimentally. It may be regarded as a hybrid form between the compound wheel-and-axle and the differential pulley or chain hoist. Although the design is simple, the analysis is not too obvious at the start, and is somewhat complicated, exhibiting coordinated angular and linear motions with constant accelerations due entirely to the weight of the movable pulley. While the analysis assumes no friction, the actual heat loss can be readily calculated from time and displacement measurements and the equivalent friction force determined. Numerous equations and numerical data are included. The system offers various challenges to student interest in classical mechanics, both on the lower-division and advanced levels. Particular experimental work is suggested and analytical exercises given for use by teachers.