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

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:

Torque

The last step is the calculation of the torque produced on the joint. The force vector is colinear to the vector \( \overrightarrow{BA} \). \(F\) is the force produced by the motor:

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

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:

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

Download

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

circle_circle_intersections.m

Matlab confirmation of the calculation of the linear motor actiated joint

See also


Last update : 05/20/2022