Unit 60: Dynamics of Machines - FREE STUDY

1 1 unit 60: Dynamics of Machines unit code: H/601/1411 QCF Level:4 Credit value:15 OUTCOME 1 MECHANICAL POWER TRANSMISSION SYSTEMS TUTORIAL 4 UNIVERSAL COUPLINGS 1. Be able to determine the kinetic and dynamic parameters of mechanical power transmission system elements Gears: gear geometry; velocity ratios of simple, compound and epicyclic gear trains; acceleration of geared systems Screw drives: motion on an inclined plane; efficiency of square-threaded lead screws and screw jacks Flywheels: turning moment diagrams for reciprocating engines and presses; determination of required flywheel moment of inertia to satisfy specified operating conditions Universal couplings: Hooke s joint; constant velocity joint; conditions for a constant velocity ratio On completion of this short tutorial you should be able to do the following.

2 Explain the principles of a universal joint. Calculate the velocity ratio. Explain a constant velocity joint. D. J. Dunn 2 1. INTRODUCTION A common problem in Mechanics is how to transmit a torque by a shaft between an input and output not on the same axis. This is solved with a Universal Coupling containing a joint known as Hooke s Joint and Hardy Spicers. These are commonly used on propeller shafts joining gearboxes to the wheels of vehicles and on hand tools to allow access to difficult places. Figure 1 You can see an animated version of a double universal coupling at this web site. 2. UNIVERSAL JOINT The diagram illustrates the basic design. The spider is a cross that is assembled into the ends so that they can pivot about two axes normal to each other.

3 Rotation can be transmitted from one to the other and the axis direction can change. Figure 2 The only problem with this arrangement is that if the input rotates at a constant rate the output does not and speeds up and slows down during each revolution. Without proof, it can be shown that if the angular velocity in is 1 and out is 2 the relationship is cos sin1cos 2212 where is the angle between the two axes and is the angle rotated by the input. This problem can be resolved if two joints are used as shown. This is called a constant velocity joint. D. J. Dunn 3 Figure 3 WORKED EXAMPLE Find the greatest and smallest values of the velocity ratio of two shafts joined with a universal coupling when the axis are at 45o. cossin1cos 2212 45cossin1cos4522 cos2/1122-1/2 When cos = 1 22 12 (Maximum) When cos = 0 21 12 (Minimum) SELF ASSESSMENT EXERCISE 1.

4 Produce a graph of velocity ratio against angle for = 45o and confirm the previous result. 2. Find and describe four mechanisms that use a universal joint.