Hi,
to calculate the forces, accelerations and velocitys, you will have to make some measurements before starting calculations.
Is there any possibility to measure the contact-time?
The punch will be not elastic in the real situation, we will loose energy.
Basically you can start the calculation with this:
You can assume a contact time of 30ms.
Considering the following as known:
There are multiple problems to be solved before taking real world measurements as:
- where are the IMU's going to be placed and why?
- how can you accurately measure the force applied by the pendulum
- what happens when multiple punches are thrown?
I started with the math the same way you did, but got stuck. Here is my progress (after many tries).
I was also thinking at analising the system as a black box and using Matlab System Identification Tool for finding the model, but then I will also need to know the applied force in order to link it to the acceleration of the bag.
The one thing that I do not understand is why is there a factor of 2x when calculating a_punch ?
Apart from that, the math seems fine for calibration purposes and testing, but what happens when a real person hits it? There's no recoil of the punch, due to the nature of the impact being plastic.
Further more, imagine someone hits the bag when it is traveling from O1 to O with enough force to stop it, but not enough force to imply a movement back to O1 (the bag practically remains almost still for some time). The equations fail to model this kind of a situation.
There's one more thing mentioned in the problem: the bag is hit in a vertical space. Judging on this, one can say it's not always hit in the center of mass. Imagine this: you hit the bag with the same force:
- 1st time closer to the base
- 2nd time closer to the top
The speed of the bag will be different between the 1st and the 2nd hit, while the force is the same. I guess one more thing that's to be taken into consideration is the torque that's applied relative to the mounting point of the base (the spring). I might be wrong, though.
Note: Due to the functions of the IMU acceleration on all 3-axis is provided as well as angle variation is time (due to gyro)
Everything looks fine, but I don't quite understand one thing: why is there a factor of 2x that is multiplied to obtain a_punch ?
The model seems pretty good for calibration and testing, but I do not think it applies for a real human punch if you take into consideration the following:
- When it comes to a real punch, there's no recoil, due to the impact being somehow plastic.
- Hitting the bag multiple times.
- Imagine you hit the bag when it moves from O1 to O with just enough force to stop it, but not enough to bounce it back to O1. The bag remains still, the velocity is 0, thus, according to the equations, the force is 0; but it obviously is not.
- Imagine you hit the bag with the same force, but the projection of force does not go through the center of mass.
- 1st time you hit somewhere near the top end of the bag
- 2nd time you hit somewhere near the bottom of the bag
In both of the above situations you hit the bag with the same force, but due to the moment of force being different you end up with a different velocity, thus two different forces computed.
Due to my limited knowledge in physics, this was the hardest part for me and still is. Finding a model that fits the entire picture.
@hgpt wrote:
- When it comes to a real punch, there's no recoil, due to the impact being somehow plastic.
- Hitting the bag multiple times.
- Imagine you hit the bag when it moves from O1 to O with just enough force to stop it, but not enough to bounce it back to O1. The bag remains still, the velocity is 0, thus, according to the equations, the force is 0; but it obviously is not.
- Imagine you hit the bag with the same force, but the projection of force does not go through the center of mass.
- 1st time you hit somewhere near the top end of the bag
- 2nd time you hit somewhere near the bottom of the bag
In both of the above situations you hit the bag with the same force, but due to the moment of force being different you end up with a different velocity, thus two different forces computed.
Due to my limited knowledge in physics, this was the hardest part for me and still is. Finding a model that fits the entire picture.
If you want all this you need a simulation tool maybe for example MAPLE-Simulation.
To make that all in MathCad, i think it's very difficult.
In a model you can setup parameters, springs, pendulums, etc and describe them with parameters like stiffness, density, viscosity and all that stuff.
There is also an option to solve this problem for example in a CAD-SolidWorks Simulation-Tool.
There you can built a modell with all components (Bag, puncher, spring, etc.) and then you can start the simulation.
You can also define diagramms for the Force, speed, acceleration for all components and movement directions as well.
I have done many simulations in that way.
Todays Engineers choose this way because it is the fastest way to find out how a mechanical system reacts when initial physical quantities act on it.
So this should be your way to solve the problem you described (of course if you have the possibility to use such a simulation software)
Calculating this manually does not really make sense.
