Inverted Spring Pendulum and Control Torque

Your drawing still makes no sense as you can't apply torque to a point contact and the arrows seem to indicate torque applied to the mass???

Do you mean like this?

Del

thanks..

Yes, sliding joint is what I ment when i say "spring is compliant only in axial direction".

you can think that the torque is generated at the pivot..

if a pure spring, there is no torque transmitted cuz spring transmits only axial force. However if I assumed the pendulum is slilding joint with spring, I can put a control torque...right ?!?

You can apply a control torque to the shaft at the bottom regardless of what is attached to the pendulum...I mean you could tie a sack of squirrels on there and still apply a control torque.
I'm still confused by statements like 'you can think that the torque is generated at the pivot..'
Surely a torque is appled to generate a movement?
Or are you saying that some external force is exciting the pendulum (not via the pivot point)? and you want to know what torque is generated at the 'pivot'...
If it's a pivot then surely there is no torque, if it's a rigid mound then there will be a force on that mount.
I still feel I don't actually know what you are asking?
I feel you need to explain EXACTLY where the forces you are interested are being applied and what you want to know.
Del
(Please someone tell me if I'm being thick here...)

please check this link : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2918273/

It's a simple walking model.

I want to add a control to the walking model. the model consists of point mass, massless legs(spring), and curved foot. (you do not need to think about curved foot.)

Can I put a torque to the model ?... sorry if you are still confused..

All too theroetical for me.
An afternoon experimenting would probably tell you more, I shall let the theorists help on this one...
Del

figure link : http://blog.naver.com/nkaier/50096159402

I thought there was a sliding joint there. Do you mean that the spring is totally floppy, like a wet noodle or a "Slinky"?

If there is a sliding joint, the rod within the barrel will transmit the torque; the spring would be a linear-only shock absorber of sorts.

Please check this out, do you find something wrong in this figure ?

figure link : http://blog.naver.com/nkaier/50096175994 ( for zooming in )

I wonder how I can draw a free body diagram of sliding joint pendulum.. (fig C-1 & C-2). Do you have any comment on it ? thanks in advance......

C-2 looks best, but I would add the telescoping joint detail shown by Del in Post 1.

telescoping leg is different from sliding joint with spring ?

In case of telescoping leg, do you think which euler equation is correct, E or F ?

Let W be the weight supported by the conceptual model, L the length of the "leg", and θ the angle of the "leg" from horizontal. Then the equilibrium torque is W L cosθ. To make this accelerate (and thereby actually move), the applied torque must be somwhat greater than that.