# Model of a rotary joint driven by a linear motor [Part 4]

## Torque

The last step is the calculation of the torque produced on the joint. The force vector is colinear to the vector $$\overrightarrow{BA}$$. Let's name the force produced by the motor $$F$$:

$$\overrightarrow{F} = F \times \dfrac{ \overrightarrow{BA} }{ | \overrightarrow{BA} | }$$

Since the vectors $$\overrightarrow{OA}$$ and $$\overrightarrow{F}$$ are know, we can use the cross product to calculate the torque on the rotary joint:

$$\vec { \Gamma } = \overrightarrow {OA} \times \vec{F}$$

$$\Gamma = F_x \times y_A - F_y \times x_A$$