Continuously Variable Transmissions (CVTs) can be used to optimize the energy utilization of systems by allowing the prime mover to operate at speeds of peak efficiency while allowing the driven components to move at desired speeds. A CVT saves energy by reducing the off-peak efficiency of a system. The basic design principles of a Continuously Variable Transmission composed of a sequence of 4-bar cranks are discussed. The vector solution for 4-bar cranks is iteratively solved for a crank sequence to illustrate how different output speeds can be obtained from the same input speed. This is accomplished by varying the length of the connecting link on each 4-bar crank in the sequence. Solutions are plotted. Each 4-bar crank is located on the same drive shaft and the same driven shaft. Each crank has the same drive link length and the same driven crank length. A one way clutch located on each driven link transmits motion to the driven shaft. The cranks are positioned so that they are out of phase with each other so that only the fastest crank transmits motion, over-running all the other cranks. For a given length of the connecting link, the motion of the driven shaft is not uniform. This is due to the 4-bar crank transmission of peak speed. As one 4-bar crank moves, at some point the angular speed of the driven link will overtake the speed of the driven link on the other crank sets. It will then peak and then slow to be overtaken by another crank-set. The more evenly distributed crank-sets used the more uniform the motion will be. In this sense, a given length of connecting link for the sequence of cranks will generate an average drive shaft speed. If the length of the connecting link in a 4-bar crank is changed, a change in motion of the driven shaft will occur. By changing the length of the connecting link on the 4-bar cranks, the average speed of the driven shaft can be changed. A CVT is made by infinitesimally changing the length of the connecting link. This infinitesimal change is easily accomplished via standard components such as pneumatic or hydraulic cylinders or various other means.
Robustness of event-based discrete PI controllers. A sampled describing function approach
