The aim of this post deals with ball joint connecting link. The following model is considered:

## Kinematic

This part explains how to calculate .

The angle will be calculated with the following relation:

First, let’s calculate the coordinates of :

Based on the previous result, let’s calculate the distance between and :

In the triangle , rectangle in , it becomes easy to calculate the angle :

Now we can calculate the angle in the triangle thanks to the Al Kashi’s theorem:

and finally:

In conclusion:

where:

## Torque

This second part explains how to estimate the torque transmitted. Let’s assume that the actuated rod is the left one (centered on ). The torque provided on this rod is . The aim is to calculate the torque transmitted () on the second rod (centered on ). The purpose of this second part is to express .

First, let’s calculate the coordinates of :

Let’s calculate the amplitude of the force :

Now, calculate the angle between and :

Let’s calulate the angles:

And :

Now can be calculated:

and can also now be calculated:

As it was done for , let’s calculate the angle between and :

The force can now also be calculated:

The outpout torque is :

In conclusion:

where:

and

## Download

**Matlab [Connecting rod] 3.22 KB**