Multiple torsion spring problem
Multiple torsion spring problem
(OP)
Will try to do my best at explaining, you can see the less-than-helpful graphic attached as well.
I have a linkage of 4 segments joined end-to-end in a straight line. Rotation at each of the three joint locations is controlled by torsion springs (all three of same spring constant). A single cable passes along all the members at a fixed distance away from the joint centers and applies the tension to cause the same moment at each joint location (similar to how tension on fishing line bends the fishing pole). I am trying to solve for the amount of cable tension required to cause each joint to rotate a specific amount of degrees.
Aaaaannnd unfortunately I'm having a complete mental lapse. I am assuming that, in this case, the 3 springs are acting as if in series (because the total cable displacement is evenly divided amongst the three springs), and therefore the Keq would be (K1*K2*K3) / (K1+K2+K3). Am I doing this right? Or am I completely off base?
Thanks!
J
I have a linkage of 4 segments joined end-to-end in a straight line. Rotation at each of the three joint locations is controlled by torsion springs (all three of same spring constant). A single cable passes along all the members at a fixed distance away from the joint centers and applies the tension to cause the same moment at each joint location (similar to how tension on fishing line bends the fishing pole). I am trying to solve for the amount of cable tension required to cause each joint to rotate a specific amount of degrees.
Aaaaannnd unfortunately I'm having a complete mental lapse. I am assuming that, in this case, the 3 springs are acting as if in series (because the total cable displacement is evenly divided amongst the three springs), and therefore the Keq would be (K1*K2*K3) / (K1+K2+K3). Am I doing this right? Or am I completely off base?
Thanks!
J





RE: Multiple torsion spring problem
Ted
RE: Multiple torsion spring problem
I have a working model on my desk so I know it works in this fashion, just not sure if the math can be simplified using springs in serial or if the situation is much more complex.
RE: Multiple torsion spring problem
RE: Multiple torsion spring problem
Working off my phone at the moment but i'll try to get a better sketch up when i'm at the computer.
Otherwise, imagine if each segment only had one eyelet square in the middle of it. as the segments rotate the eyelets would move closer together, eventually touching each other if allowed to complete full 180 degrees of rotation. This would allow for cable shortening. My 'eyelets' are just set closer to the joint center(s) to reduce amount of gapping between segments and cable, and reduce cable excursion necessary to rotate segments.
Again. really sorry my descriptions are falling short as I know this physically works with a working model. Just feel my explanation is letting me down in accurately explaining setup. I'll see if I can get a better pic or sketch up at some point.
RE: Multiple torsion spring problem
RE: Multiple torsion spring problem
The multiplication of joints will see a multiplication of the amount of cable pulled, not the tension required. Since the tension is a function of angle, but the amount is a linear function of the number of joints, then more joints just means more cable, acting just like series tension springs.
RE: Multiple torsion spring problem
In the end, just looking to size my cable and power source that generates the tension. Hoping to use some simplified model & assumptions (e.g assuming eyelets are close enough to joint centers to keep lever arm essentially constant, even though some gapping and lengthening of lever arm will occur) to get a 'worst case' estimate, which should ensure adequate choices for both.
Glad to here the series assumption holds water, this certainly makes my life much easier. Thanks for the help!
RE: Multiple torsion spring problem
Elasticity in the cable and effects of friction at several eyelet contacts in series will make your analysis more complicated.
RE: Multiple torsion spring problem
Cable stretch and friction are more my worries w/ how big of a factor they may play:
Glad you brought up elasticity. I was planning on using heavy fishing line but can only get monofilament here, so after your comment did some testing and got 10%-20% stretch - yikes! Will probably switch to something like bike control cable that has an elastic stretch in ranges I can tolerate.
May end up having to throw cable friction into the equation, but in a reasonable manner that doesn't cost me more in time than the cost of a few trial-and-error iterations.
RE: Multiple torsion spring problem
What if you varied a cylinder size? Would this be akin to lengthening one of your string connectors? This is the finger gripping mechanism that I haven't studied yet.
RE: Multiple torsion spring problem
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