Mass on a stick model.

  • Thread starter Integral
  • Start date
  • #1
Integral
Staff Emeritus
Science Advisor
Gold Member
7,200
56

Main Question or Discussion Point

I have need of a mathematical model of a mass at the end of a stick, pivoting about the opposite end. What I have done so far is not giving realistic results, would appreciate it if some one could point out my error.

Basic model :

[tex] \tau = I \ddot {\theta} [/tex]

[tex] I = m r^2 [/tex]

The system is being pushed by an air cylinder (force F) with the fixed end mounted a distance L directly below the pivot, the moving end of the cylinder is mounted a distance r along the pivot arm from the pivot point. With [itex] \phi [/itex] the angle between the cylinder and the pivot arm. So I have :

[tex] \tau = r F sin( \phi) [/tex]

My variable of interest will be the angle between the pivot arm and the line defined by the pivot and the fixed end of the cylinder, call this angle [itex] \theta [/itex]

By the law of sines I get

[tex] \frac {Sin(\phi)} {L} = \frac {sin(\theta)} {x} [/tex]
where x is the length of the cylinder.

I get x in terms of [itex] \theta [/itex] from the law of cosines

[tex] x^2 = L^2 + r^2 -2lr cos(\theta) [/tex]

The differential equation is:

[tex] \ddot{ \theta } = \frac { \tau } {I} [/tex]

See the attachment for a diagram.
 

Attachments

Answers and Replies

  • #2
Integral
Staff Emeritus
Science Advisor
Gold Member
7,200
56
Ok, The above model is correct. For the last week I have been running this through an excel spreadsheet using a Runga Kutta method, the results were not correct, the system simply did not respond the way I KNEW it should.

My error? using the fricking English measurement system. I was using lbs where I needed slugs. So I was throwing 32 times the mass I thought I was. That sort of slowed things down. I finally made the simulation work by changing everything to metric, Newtons for force, kg for mass and meters everywhere, It worked great. It was then that I seriously began to figure out the lbs mass lbs force issue.
 

Related Threads on Mass on a stick model.

  • Last Post
Replies
2
Views
5K
Replies
9
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
14
Views
1K
Replies
6
Views
31K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
2
Views
659
  • Last Post
Replies
8
Views
1K
Replies
9
Views
4K
Top