1.0 GENERAL

A universal joint is a positive, mechanical connection between rotating shafts, which are usually not parallel, but intersecting. They are used to transmIt motion, power, or both.

The simplest and most common type is called the Cardan joint or Hooke joint. It is shown in Figure 1. It consists of two yokes, one on each shaft, connected by a cross-shaped intermediate member called the spider. The angle between the two shafts is called the operating angle. It Is generally, but n01 necessarily, constant during operation. Good design practice calls for low operating angles, often less than 25°, dependIng on the application. Independent of this guideli ne, mechanical interference In th e construc tio n of Cardan joints limits the operating angle to a maximum (often about 37½°), depending on its proportions.

2.0 Applications

Typical appllcatlons of universal joints include aircraft, appliances, control mechanisms, electronIcs, Instrumentation, medical and optical devices, ordnance, radio, sewing machines, textile machInery and tool drives.

Universal joints are available in steel or in thermoplastic body members. Unlversal joints made of steel have maximum load-carrying capacity for a given size. Universal joints with thermoplastic body members are used in light industrial applications in which their self-lubricating feature, light weight, negligible backlash, corrosion resistance and capability for high-speed operation are significant advantages.

Universal joints of special construction, such as ball-jointed universals are also available. These are used for high-speed operation and for carrying large torques. They are available both in miniature and standard sizes.

3.0 General Characteristics of the Cardan Joint

A basic characteristic of the Cardan joint is the nonuniformity of motion transmission through the joint. The angular-velocity ratio between input and out put shafts varies cyclically at two cycles per revolution of the input shaft. This fluctuation, which is accompanied by corresponding angular accelerations, increases with the operating angle and can be as much as 15% of peak angular velocity (in the case of a 30° operating angle). In selecting a joint the effect of these fluctuations on static torque, inertia torque and system performance needs to be kept in mind.

The non uniformity of the transmission can be eliminated by using two appropriately phased universal joints in series, as shown in Figure 2. In such cases the velocity variation induced by one joint can be made to cancel that of the ot her, thereby transmitting a constant (1:1) angular velocity ratio between shafts. The angular velocity fluctuation of the intermediate shaft, however, cannot be avoided. Two universal joints in series also permit coupling of two laterally displaced shafts (single Cardan joints are limited to intersecting shafts).

Single Cardan joints have the following advantages:

• Low side thrust on bearings.
• Large angular displacements are possible.
• High torsional stiffness.
• High torque capacity.

They have the following disadvantages:

• Velocity and acceleration fluctuation increases with operating angle.
• Lubrication is required to reduce wear.
• Shafts must lie in precisely the same plane.
• Backlash difficult to control.

4.0 Kinematics

For a uniformly rotating input shaft, the output shaft angular – velocity and angular acceteration undergo two cycles per revolution of the input shaft. The angular displacement of the output shaft does not precisely follow that of the input shaft but leads or lags, again with two cycles per revolution. The angular-velocity variation as a function of operating angle is illustrated in Figure 3.

The peak displacement lead (or laq). peak angular-velocity ratios (max. and min.) and peak angular-acceleration ratios are shown as a function of operating angle in Table 1, which is reproduced from “The Analytical Design of Universal Joints” by S.J. Baranyi, Design News, Sept. 1, 1969.

The table should always be consulted for exact numerical values. As a qualitative guideline, it may be kept in mind that for small operating angles (say up to 10°), the angutar-displacement error (max. lead or lag), the deviation of the max. and min. angular velocity ratios from unity, and the maximum angular acceleration ratio are very nearly proportional to the square of the operating angle.

The static torque transmitted by the output shalt is equal to the product of the input to torque and the angular-velocity ratio. The angular acceleration gives rise to an inertia torque, as well as to vibrations. The inertia torque typically would be equal to the sum of the product of the angular acceleration of the output shaft (rad/sec²) and the polar mass moment of inertia of the output shaft (in-lb-sec²) and the output torque (with the units indicated the torque would be given in in-Ibs).

The inertia loading often determines the ultimate limit on the speed of operation of the joint. Recommended speed limits vary depending on operating angle, transmitted power and nature of the applicatlon. Recommended peak angular accelerations of the driven shaft vary from 300 rad/sec² to over 2000 rad/sec² in power drives. In light instrument drives, the allowable accelerations may be higher. For an accurate determination of allowable speed, a stress determination is necessary.