Darshan institute of engineering & technology

RATIO OF ANGULAR VELOCITY OF SHAFT OF HOOK’S JOINT PATEL RAM (130540119078)

Introduction This joint was first invented by Da Vinci, an English physicist and mathematician Robert Hooke's (1635-1703) name is associated with it since he put it to use for connecting two non-parallel and intersecting shafts. It is commonly knows as 'Universal Joint'.

It is used for transmitting power from engine gear box to the rear axle of the automobile. It is also used in knee joint of a milling machine. The angle between the driving and driven shafts may be constant but usually it varies while the vehicle moves on an uneven surface.

One of the disadvantages of this joint is that the velocity ratio is not constant, because the driving shaft rotates at a uniform angular speed but the driven shaft rotates at a varying angular speed. Because of variation in the output speed (driven), single Hooke's joint is not recommended for high speeds as it may cause excessive vibrations in the system. To have constant velocity ratio, double Hooke's joints are used.

The universal joint consists of two shafts '1' and '2' known as the driving and the driven shafts respectively. These shafts rotate in fixed bearings. Each shaft carries a semicircular fork at its end. The angle between the shafts is assumed as 'α'. The ends of the forks are connected by a center piece, which is in the shape of a cross, sphere or square. This cross has four arms which are at right angles to each other. The fork ends of the driving shaft T are 'A' and 'B’ and that of driven shaft '2' are 'C' and 'D’.

Angular Velocity Ratio The velocity ratio can be determined from the following formula: Where: α is the angle between the shafts

 

 

Maximum and Minimum speeds of the driven shaft.   The speed variations of the driven shaft are shown on the polar diagram as shown

 

Condition for Equal speeds. This condition is satisfied at four points 5, 6, 7 and 8

Maximum Variation of speed. Here, it should be noted that if the speed of the driving shaft is N1 r.p.m then in the above relation N1 may be in place of ω1

Angular Acceleration of the Driven Shaft.