This post explain and describe the model of a rotary joint actuated by a linear motor, or an air cylinder. The goal of this model is:

- to compute the angle of the rotary joint according to the actuator length ;
- to compute the torque on the joint according to the actuator force.

Here are our hypotheses:

- The length of the motor \( | \overrightarrow{AB} | \) is known
- The offset of the motor \( | \overrightarrow{BC} | \) is known and fixed
- The length of the lever arm \( | \overrightarrow{OA} | \) is known and constant
- The length of the frame \( | \overrightarrow{OC} | \) is known and constant
- The triangle \( ABC \) is rectangle in B
- The motor produces a force \( F \)

This article is splitted in tour parts:

- Angular and linear velocity, cross product
- Configurable gear for solidwork
- Elastic collision - Part 1 - Hypotheses
- Elastic collision - Part 2 - Velocity decomposition
- Elastic collision - Part 3 - Velocity calculation
- Elastic collision - Part 4 - Synthesis and reminder
- Elastic collision - Part 5 - Source code
- Elastic collision - Equations and simulation
- Enable Add-Ins in Solidworks
- Newton's Second Law of motion
- Geometric model for differential wheeled mobile robot
- How to insert gears in a Solidwoks assembly
- Mathematical model of a mechanical differential
- 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 [Part 4]

Last update : 10/08/2022