Equations of this kinematic system for Theory of Machines subject.

[kajukaa]

Hello everybody,

I need to write all the equations for each component for this kinematic system. Then, I will need to calculate velocity, acceleration and displacement.

Would you be able to help?

 

[rb1957]

for a given omega, you can define the point (the center of the small block) in terms of r, phi, and omega and omega-dot.

vector "j" is a bit tricky, but you should be able to determine the mag and arg of the vector.

the orientation of the block is a little tricky.

i assume point "d" is limited to vertical motion.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[kajukaa]

Hello rb1957, actually I realized I haven't even given the assumptions and parameters of the system. Let me share with you, in case it would help you and me so solve them:

 

[rb1957]

equations of motion describe how the parts of the system move/change as some governing input changes, like y = f(x). here the governing input should be the angle "phi" and omega (omega can't be constant, unless the arm rotates 360 degrees. It can have a momentary value, but for me the position and motion of "B" should be determined by phi and omega. For example, the length of "3" is R+h when phi = 0 and something less as phi increases (when phi = 30deg, L3 = sqrt((R*cos 30)^3+(h +R*sin30)^2) ... yes ?

and D is at R+a+b when phi = 0

clear as mud ?

have you tried solving easier problems first ?

have you read (and understood) the text ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[kajukaa]

Hello rb1957,

Sorry I'm a beginner in theory of machines. In this case omega w is given as constant which means the arm rotates 360 degrees (angular velocity is const.). In order to calculate position and motion of B, I though angular velocity as first would be calculated as w(omega) = r x phi ? I'm trying to solve easier ones now before I move to this one.

 

[rb1957]

no ... omega is really phi_dot. phi and r give you the cartesian co-ords of the end of the radius, pt B ?

does B slide along 0-C ?
is "a" the length of the slider, or is "a" a fixed length between B and C ?

ok, you're a beginner, fine, we all start at square 0. What have you read about mechanisms ?
don't expect we (well, me) will post the answer to the problem, that IMHO doesn't help you learn.

if omega is constant then the radius rotates about 0 and you can determine the co-ords of the end of the radius as a function of time. As you know, the end of the radius moves with a speed of omega*r. As the end of the radius moves, how does length 3 change ? look at some "obvious" positions, run excel with many values of phi. how long does it take for phi to change by 1 degree ? plot the results, some patterns may become visible. how does pt C and D move ?

GL

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[GregLocock]

Are you solving this graphically using velocity diagrams - in which case i can't remember anything, or by geometry?

If the latter

Get the position of B as a function of phi
get the position of C as a function of the position of B
get the position of D as a function of the position of C

None of that is anything more than basic trig.


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[kajukaa]

Hello Greg, I need to solve them graphically using the diagrams of velocity, displacement and acceleration in python. So, in reality I should write all the equations to solve the current state of the system and then make it possible for other values to work as well.

 

[mecademie]

I hope you find success in solving your problem. I wanted to share a video that I believe will be extremely useful for you. The solution explained in the video addresses a problem very similar to yours, focusing specifically on velocity analysis.
Please take a look and let me know if you find it helpful. Here is the link:

https://www.linkedin.com/feed/updat...60?utm_source=share&utm_medium=member_desktop