as a function of deflection angle ß

Phi 1 = Input – rotation angle
Phi 2 = Output – rotation angle

If a single joint is deflected by angle ß and rotated in this condition, rotation angle j2 of the output shaft differs from rotation angle j1 of the input shaft. The relationship between the two rotation angles is as follows:

As can be seen from the adjacent diagram, maximum lead occurs at about 45°, maximum lag at about 135°.
Fork position Phi 1 = 0°
is then obtained, when the input fork is located in the deflection-plane of the joint.

as a function of deflection angle ß

MdI = Input torque
MdII = Output torque
Omega I = Input – angular velocity
Omega II = Output – angular velocity

When analyzing the motion and torque characteristic of a singular joint, it is found that with a constant angular velocity- and torque input, a fluctuating motion and torque curve is obtained at the output. The reason for this fluctuation can easily be illustrated by following the torque characteristic at the fork position Phi 1 = 0° and Phi 1 = 90° as shown at left. Since the torque can only be transmitted in the spider plane, the spider however, depending on the fork position, is always at a right angle to the input or output axis, output torque fluctuates twice per revolution between MdI · cos ß and MdI/cos ß.

The transmitted power, however, is constant disregarding friction losses in the bearings.

Therefore, the following applies:

For fork position Phi 1 = 0°
we obtain:

and for fork position Phi 1 = 90°:

as a function of deflection angles ß1 and ß2

Section 2.2 illustrates that angular velocity and torque at the output of a single joint
follow a sinusoidal pattern with a 180° cycle. Maximum angular velocity wII max max coin-cides with minimum torque Md II min andvice versa. From this can be derived that a uniform output is then possible,when a sec-ond joint, having a 90° phase shift is connected tothe first joint by means of a shaft. Then, the non-uniform motion of the first joint can be balanced by the non-uniform motion of the second joint. The required 90° phase shift is always then met, when the two inner forks happen to be in the deflection plane of their respective joints. Moreover, the two deflection angles ß1 und ß2 of both joints must be the same. (See also Section 1.1 and 1 .4).

With unequal deflection angles, complete compensation is not possible.
For ß2 > ß1 the following applies: