This paper employs control techniques to analyze kinematic relationships via block diagrams for planetary gear systems. The revealed tangent-velocity equations at each contact point of the mechanical gearsets are utilized to plot the block diagrams. Then, the concepts of feedback and feedforward strategies are adopted to illustrate speed-reduction and increasing functions in kinematics with sensitivity analysis. The structural difference between unusual planetary gears and common ones is also explained based on the characteristic equation of feedback strategies for structural constraints in terms of stability conditions. A cam-controlled planetary gear is further illustrated for the constraint and kinematic analysis by using the block diagram technique and characteristic equation, and the computational simulations for the sensitivity and the motion output of this planetary gear are obtained. Through the correspondence between control and kinematics, this paper provides a guide for engineers in various fields to easily understand the function of mechanical design.
A simple and useful procedure that can be used to determine profile surfaces of planar and spatial cams with cylindrical roller-followers is presented. Based on the rigid-body transformation between the cam and the roller-follower, the pitch (curve) surface which is the path of the point of the roller centre can be easily generated. Then the analytical profile surface of the cam can be represented by the offset surface of the pitch surface with a distance equal to the radius of the roller. T o illustrate the ease and effectiveness of the approach, analytical expressions of profile surfaces of a disc cam, two cylindrical cams and two globoidal cams are typically given. Furthermore, in order to show the validity of this method, the results are then compared to those derived by an earlier procedure based on the screw theory.
A simple, yet useful approach to the geometry design and machining of globoidal index cams and roller-follower turrets is developed. From the machining point of view of the globoidal cam by an end mill, the side surface geometry can be easily defined as the swept surface by the tool path. By using the analytical cam surface formulation, the pressure angle, the contact forces, and the torques between the cam and the turret can be investigated. In the machining process, to avoid undercutting, principal curvatures are analyzed. To demonstrate the usefulness and effectiveness of the procedure, two numerical examples of the globoidal index cams are presented along with the 3D computer printouts and the photography of machined samples.
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