# Universal Joint

Rotational coupling between two driveline shafts

**Library:**Simscape / Driveline / Couplings & Drives

## Description

The Universal Joint block represents a rotational
coupling between two driveline shafts. The coupling transfers torque between the shafts
so they spin as a unit under an applied load. Two rotational degrees of freedom,
internal to the coupling, allow the shafts to connect at an angle. This intersection
angle varies according to the physical signal input from port **A**.
Optional compliance, modeled as a parallel spring-damper set, allows the coupling to
deform under load.

You can use the Universal Joint block as a connection between two rotational driveline components—for example, between the driving and driven shafts in an automobile drive train.

The ratio of the shaft angular velocities depends on two parameters: the intersection angle between the two shafts and the rotation angle of the base shaft. A physical signal input provides the intersection angle while a property inspector parameter provides the initial base shaft angle. These two angles fix the ratio of the two shaft angular velocities according to the nonlinear equation:

$${\omega}_{F}=\frac{\mathrm{cos}(A)}{1-{\mathrm{sin}}^{2}(A)\cdot {\mathrm{cos}}^{2}({\theta}_{B})}{\omega}_{B},$$

where:

*ω*is the angular velocity of the follower shaft about its length axis._{F}*ω*is the angular velocity of the base shaft about its length axis._{B}*θ*is the rotation angle of the base shaft about its length axis._{B}*A*is the intersection angle between base and follower shafts about the base shaft pin.

The two schematics in the figure illustrate the equation parameters. In each schematic, the left shaft represents the base shaft, while the right shaft represents the follower shaft. The right schematic shows the coupling seen in the left schematic after the shafts spin 90° about their length axes (dashed line segments).

In the figure, the intersection angle is the angle between the two
shafts about the pin of the base shaft. The absolute value of this angle must fall in
the range `0 ≤ A < Maximum intersection angle`

. The base shaft angle
is the angle of the base shaft about its length axis. The base shaft angle is also the
time-integral of the base shaft angular velocity,
*ω _{B}*.

## Ports

### Conserving

### Input

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2013b**

## See Also

Belt Drive | Belt Pulley | Chain Drive | Flexible Shaft | Rope Drum