I must say that I completely lost track now with the PE = 0 at the fulcrum.
I just put your integral into wolfram and I'm getting the same values as with ## PE_{rod} = m_rgr(0.5-0.5cos\theta) ## but also there I'm not sure if I did it correctly...
I'm sorry, but this confuses me.
The change in height is ## \frac {r} {2} - \frac {r} {2} cos\theta = \frac {r} {2} (1 - cos \theta) = r (\frac {1}{2} - \frac {1} {2} cos \theta) ## as I've seen it in different pendulum and physical pendulum problems.
Change in height from ## \theta_o ## to ##...
That would be the case if the rod is falling to the ground? The CoM of the rod can just 'fall' r/2 and therefore for me it should be ## PE_{rod} = m_rg\frac {r} {2} (1-cos\theta) => m_rgr(\frac {1} {2} - \frac {1} {2} cos\theta)##
And I will try the integration and see what I'm getting as a...
Shouldn't it be ## PE_{rod} = m_r r g ( \frac {1} {2} - \frac {1}{2} \cos \theta ) ## ?
This results in the same equation I had, just written a little different? However, with ## \kappa ## there is still the fact that you provide the starting angle ##\theta_o## and the contact angle ##\theta## ?
So I would have to find an equation where ω(θ) is just solved by giving the starting angle?
I'm having trouble to get my head around this, as different starting angles result in different velocities, because of different starting energies. E.g. starting at angle θ = 80° and ending at θ = 20°...
I'll try to write my steps in detail.
- mass of the bob = 2.332 kg
- mass of one rod = 1.72 kg
- nbr rods = 4
- length of rod = 0.9m, width = 0.025m
- radius turning axis to bob = 0.85m --> 0.85/2 = 0.425 radius from CoG of rod to axis.
- angle before impact ##\theta_c## = 20°
Potential...
Thank you, but I'm having quite some trouble calculating it.
Let's take the potential energy of the bob and rods together which would then be ## m*g*l*(1-cos(θ_i)) ##, the PE at contact would be ##m*g*l*(1-cos(θ_c))##.
The equation for the angular velocity ω would be ##ω = \sqrt {\frac...
It's the tangential acceleration which causes the change in velocity? Is there any method to find out how much time t is needed to reach the velocity at a certain point when starting from v = 0?
My first approach would have been:
t = θ*2/ω
but this is only for a constant acceleration.
The...
Well, I think I've found the mistake.
I used video analysis to measure the velocity based on the fps, but I took the average velocity (ω = θ/t) instead of the velocity at the specific point I did the computation for.
Now the question is, if it is a constant acceleration or a changing acceleration?
Hello People, it's me again.
First of all, thank you for your suggestion Baluncore and sorry that I didn't answer anymore. However it isn't possible for me to build it like this.
Second: I've got quite a difference in the calculated linear velocity of the bob vs. the actual measured linear...
It just works because of the twisting and rotation of the bob > 90° is possible due to enough play in every axis and because the construction lacks a great amount of precision. However I have done some finetuning to the mechanism, based on your input and now it effectively shows a behaviour that...
The device should simulate an impact + sliding over a very short distance. The first idea was a pendulum with 1 rod, however this wouldn't keep the attachment level. Therefore the 4 bar 'parallel' linkage.
The 3 bars are a result of the construction: rod AD is mounted on the middle of the D axis...
What do you mean by backed? The upper plate is fixed to the swinging rods. The lower plate is fixed via a linear rail system to the upper plate. So its only movement path is up and down (y axis), can't go left/right, front/back. I would say the impact is only backed by the lower mass and not the...
Thank you very much Baluncore and erobz !
If possible I would like to ask a further question, now that I am able to calculate the velocity.
The attachment on the linkage consists of 2 plates. An upper and a lower plate. The lower plate can move up and down freely. It is intended that the lower...
I didn't mean the total MoI, but just the one of the bob.
For the rod, as you described, the distance of an axis parallel to the axis of rotation is taken into account.
Why isn't this the case for the bob? Is this because the bob is just treated as a point mass? What if the bob isn't treated...