Learning Forum

[Junaidvali Shaik]

I have considered a compound double pendulum (B1, B2) with gravity, and collected CG accelerations of B1 and B2 (Acc. Probes), joint probe total forces at joints. Then I tried to calculate CG accelerations using the Force Balance equation in terms of inertial frame. However, I can not obtain calculated acceleration data as per acceleration probes. What am I missing here?

[peteroznewman]

Please provide a detailed explanation of the Force Balance equation and the input values. Include images of the model and a figure to explain all the terms in the equation.

[Junaidvali Shaik]

PFA.

[peteroznewman]

Is the pendulum sitting there motionless or is it swinging?

If it is motionless, the accelerations are zero and the force balance is a statics problem.

If it is in motion, there are rotational accelerations and angular velocities acting on the mass moments of inertia and mass that you have not included in the equations. They contribute to the joint forces, which should have a vertical and horizontal component.

[Junaidvali Shaik]

It is in motion; I am considering Force balance and moment balance equations separately for each body. Hence, M1 and M2 in the equations are just scalars (or diagonal matrices of M1 and M2).

 

[peteroznewman]

Here is a paper on the equations of motion.

These two YouTube videos cover the equations of motion.

https://www.youtube.com/watch?v=eBg8gof1RBg

https://www.youtube.com/watch?v=QE1_H2vtHLU

[Junaidvali Shaik]

PFA.

I am not looking for equations of motion; I am trying to understand force balance equations for translational accelerations of CGs.

[Junaidvali Shaik]

Please help me in this regard; I need to solve a more complicated problem with more links than two. I need the correct forces for my analysis in the inertial frame.

[peteroznewman]

I use Ansys Rigid Dynamics to calculate the motion of multiple links and you have done the same with the double pendulum.  The software allows me to create joints, apply loads such as gravity or applied forces, moments or enforced motions and solve the model to obtain information on the the motion from the simulation. I can obtain results that tell me the internal forces in the mechanism.

I don't understand what you mean by "the correct forces ... in the inertial frame".  Here is the definition from Wikipedia.

An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed.

Why don't you just build the simulation of the more complicated problem?