Dynamics holonomic nonholonomic constraint equations

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iolantham
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Homework Statement


Please see the attached file for the problem and figure.


Homework Equations



The Attempt at a Solution


This is what I have so far:
The position vector of the block, pblock= xblock wx+ yblock wy
pblock dot omegaz=0 holonomic constraint equation (dot product)
n=3N-M
N= # particles=1 block
M=# holonomic constraint equations=1
So, n=3-1=2
For the nonholonomic constraint eq.:
ur=sum Ars us + Br, with r=p+1, ..., n
Ars and Br are functions of the parameteres q1 (usually angle), q2, ..., t (time)
p=# deg. of freedom
ur=generalized speeds

For part c), I wrote omega1 r1=omega2 e => omega2=omega1 r/e=10 r/e
Thank you in advance!
 
Attachments
  • Diagram of a planar mechanism with link 1 pinned at a base and a block sliding on link 2, showing unit vectors u and v, reference frame W, angles theta 1 and theta 2, lengths r0, r1, r2 and offset e.
    dynamics exercise 001.jpg
    66.8 KB · Views: 557
No need to reply. I got the answer.

iolantham said:

Homework Statement


Please see the attached file for the problem and figure.


Homework Equations



The Attempt at a Solution


This is what I have so far:
The position vector of the block, pblock= xblock wx+ yblock wy
pblock dot omegaz=0 holonomic constraint equation (dot product)
n=3N-M
N= # particles=1 block
M=# holonomic constraint equations=1
So, n=3-1=2
For the nonholonomic constraint eq.:
ur=sum Ars us + Br, with r=p+1, ..., n
Ars and Br are functions of the parameteres q1 (usually angle), q2, ..., t (time)
p=# deg. of freedom
ur=generalized speeds

For part c), I wrote omega1 r1=omega2 e => omega2=omega1 r/e=10 r/e
Thank you in advance!