Replacing Simscape's gimbal joint's Spring Stiffnes with External Torque

Question

Ondrej Zoufaly 2024-5-16

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https://ww2.mathworks.cn/matlabcentral/answers/2119556-replacing-simscape-s-gimbal-joint-s-spring-stiffnes-with-external-torque

回答： Shishir Reddy 2024-8-28，6:31

Hello,

I tried to understand how gimbal joint's Spring Stiffnes work, so I tried to replace the Spring stiffness with external torque and the results are not equal.

Here is what I tried:

This is a 3D pendulum with gimbal joint. The upper gimbal joint has 3 spring with stiffnes k for all the coordinates (x,y,z). The lower gimbal joint's spring stiffnesses are zero but there is an External torque with the value of -k*coordinate acting on the following body (this I thought would replicate the springs in the gimbal joint) as shown in the following figure.

When I simulate the pendulum such that it rotates only around one axis it works perfectly and there is 0 error between the upper and lower model. However, when I try to simulate a general motion then there is error between upper and lower model. I tried to set the external torque resolution frame both to World and Attached Frame but I just couldn't figure out how to replicate the springs with external torque.

Do you have any idea or link to how the Springs in the gimbal joint works ? Thank you, Ondrej.

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Answer 1

Shishir Reddy 2024-8-28，6:31

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Hi Ondrej

The ability to replace joint behaviour with external torques depends on the complexity of the motion and the degrees of freedom involved.

In case of single degree of freedom, (e.g. a revolute joint) which only allows rotation around one fixed axis, it’s behaviour can be easily replicated with an external torque applied around that axis. Since the motion is constrained to a single plane, it’s easier to calculate and apply the necessary torque to achieve the same effect as the joint's inherent motion.

Therefore, when you simulated the pendulum such that it rotates only around one axis, it worked perfectly without any error between upper and lower model.

But, as gimbal joint allows rotation around three perpendicular axes, providing full 3D rotational freedom, replicating this behaviour with external torques is more complex because of nonlinear dynamics and axis coupling. The rotation around one axis can affect the other axes due to the coupling inherent in a gimbal joint, which cannot be replicated using external torque.

Therefore, for accurate simulation especially in case of gimbal joints, replicating the model with external torques is not recommended.

I hope this resolves the issue.