This page is part of an article about rotary joint driven by a linear motor. Please, start by reading the introduction.

This article is splitted in three parts:

- Part 1. Introduction
- Part 2. Angle as a function of length
- Part 3. Coordinates of 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:

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

From this page, we can deduce:

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

The Matlab script bellow has been used to check the equation presented on this page:

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- Elastic collision - Part 2 - Velocity decomposition
- Elastic collision - Part 3 - Velocity calculation
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- Elastic collision - Part 5 - Source code
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- Model of a rotary joint driven by a linear motor [Part 2]
- Model of a rotary joint driven by a linear motor [Part 3]
- Model of a rotary joint driven by a linear motor

Last update : 11/02/2022