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Countering Gravity - Physics Question — Parallax Forums

Countering Gravity - Physics Question

Kirk FraserKirk Fraser Posts: 364
edited 2014-03-03 09:14 in General Discussion
If I have a long arm controlled by a Propeller running a trapezoid program, when it goes up there is no problem from adding weight to the end except a little more slowness. When it goes down, the weight can cause the arm to descend much faster than the trapezoid curve tells it to, after it gets past top dead center. Obviously some intermittent push in the up direction is needed to allow it to descend according to the trapezoid program instead of by gravity, and to stop where requested. I'm guessing some position feedback formula is needed or some generic push back based on 32ft/s/s to neutralize gravity's effect. How should I be thinking of it to see an answer?

Also, how does gravity impact the arm if it is rotating around the down 6 o'clock position? When it goes forward or back gravity acts the same when resisted going to 3 o'clock or 9 o'clock (or higher), slowing with increased work at those perpendicular positions but when coming down the gravity increases the speed beyond the trapezoid and overshoots the stop position. So if I send out an intermittent hold in the up position signal proportional to the angle to counteract the force at that position then follow with the continuation of the trapezoid down signal, would that work or does it need a new trapezoid ramp for each several millisecond hold and restart down segment?

Now if the arm is moving in a horizontal plane where gravity has no effect, then the motions should exclude compensation for gravity. Is there a way to tell from sensing the acceleration of measured position distances if the arm is working in a horizontal or vertical plane? Or at an angle between horizontal and vertical?

It would seem so but I'm not a math whiz so please explain. Thanks.

Comments

  • FranklinFranklin Posts: 4,747
    edited 2014-02-28 21:05
    Could you provide more info like the length of the arm, the weight, the motor type and specs?
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-02-28 23:30
    length of the arm - 3 ft
    the weight - 250 lbs
    the motor type - hydraulic rotary actuator
    specs - 3,000 PSI 0-20 GPM est.

    Also I've noticed periodic surges in hydraulic power so the time to achieve 6 o'clock to 12 o'clock motion can vary by about double speed every 3 cycles. I have obtained a flow limiter valve for that purpose but haven't tested it yet.
  • Beau SchwabeBeau Schwabe Posts: 6,566
    edited 2014-03-01 00:04
    What kind of weight are you counter balancing with? ... and where is that weight located? If you think of it in terms of a wheel, if you are correctly counter balanced then all you should be dealing with is mass inertia to stop and start. It shouldn't matter what angle you are at with relation to gravity or where you are on the hands of a clock.
  • Mark_TMark_T Posts: 1,981
    edited 2014-03-01 03:38
    If I have a long arm controlled by a Propeller running a trapezoid program,
    And what exactly is a trapezoid program? A trapezoid is a quadrilateral with two unequal parallel sides and a mirror
    plane, you are describing a motor and a weight. Perhaps some more details of the linkage would help us?
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-03-01 07:41
    There is and can be zero counter balance any more than exists with your biological arm. The weight is located at one end of the arm and the motor at the other, as if you were exercising with weights. The weight may vary from 250 lbs. If you lift a weight from ground to overhead without varying the length of your arm by bending at the elbow, you'll soon understand were in the motion gravity affects the torque on your arm most.

    The mass inertia is what requires a trapezoid power curve to ramp up acceleration from zero to a stable speed as the weight is moved, then ramp down the acceleration as it smoothly achieves its final position. Without the ramp, using a square wave, there would be jerk with instant starts and stops. With this mass inertia, the jerk is so intense it can pull a motor hoist bolted to cement, out of the cement and hop around. So a smoother acceleration / deceleration is required, whether trapezoid which is common or an S-curve.
  • FranklinFranklin Posts: 4,747
    edited 2014-03-01 14:02
    What type of speed/position/rotation/angle sensors are you using to keep track of the arms position in the arc?
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-03-01 14:24
    Currently I'm working with these 10K potentiometers. http://www.digikey.com/product-detail/en/3382H-2-103/3382H-2-103-ND/2537741

    I was hoping to move up to the AS5055 magnetic sensor but the consultant increased his price by an order of magnitude.
  • FranklinFranklin Posts: 4,747
    edited 2014-03-01 19:13
    DigiKey has them for $6.48 in singles
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-03-01 19:45
    So they went up too. What I meant was the guy who was writing the Prop software started but wants lots more to finish.

    Now back to the Physics Question. How do I compensate for gravity? Thanks.
  • Beau SchwabeBeau Schwabe Posts: 6,566
    edited 2014-03-01 19:56
    Without countering, the balancing equation becomes much more complex. At 250lbs on your moment arm of 3ft, that's a lot of mechanical wear and tear at the pivot point, not to mention a massive amount of torque produced. Is the arm "fixed" or is it attached to a body that could potentially be in motion? (<-- Adding more complexity) ... Yes, opposing muscle groups work together on a human, but your not dealing with the amount of weight on a human body that you are describing with this mechanical arm. You should look into Myography and measure the effects of human muscles under varying weight conditions and positions to get a feel for a characterization load curve. Trapezoid works for ramping up speed and ramping down speed with minimal overshooting, but there are other factors at play here that should allow the trapezoid to dynamically shift based on speed, orientation, weight change, etc.
  • LawsonLawson Posts: 870
    edited 2014-03-01 21:02
    That's a large Hydraulic actuator you've got! What kind of valves do you have controlling that actuator?

    Marty
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-03-01 21:39
    Beau Schwabe (Parallax) wrote: »
    Trapezoid works for ramping up speed and ramping down speed with minimal overshooting, but there are other factors at play here that should allow the trapezoid to dynamically shift based on speed, orientation, weight change, etc.

    Yes that's part of what I need but also the valve being a Sterling two sided (A B) proportional valve presents a problem of using the trapezoid at all. Once the down motion is initiated by the trapezoid controlling the B side of the valve, gravity takes over and the control trapezoid is ignored by the weighted motion. The A side of the valve powers upward motion. So it appears there needs to be some kind of interplay between the A and B sides of the valve to accomplish getting the weight down according to the requested trapezoid motion instead of by the law of gravity. My original question was what is that interplay?
  • T ChapT Chap Posts: 4,223
    edited 2014-03-01 21:58
    It might be easier to accomplish if the hydraulic rotary output had a ratio instead of directly coupled. With a cable or pulley method, you will have a much better holding torque as a result when the pulley on the hydraulic out is smaller, even as little as 2:1 would make a big difference in stability.
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-03-01 23:06
    Pulley systems - extra complexity, possible fragility when doubling the weight, likely speed reducer.
  • Beau SchwabeBeau Schwabe Posts: 6,566
    edited 2014-03-01 23:55
    " My original question was what is that interplay? " - Myography might be an eye opener in answering that question. In your reference to A side and B side, the drive is NOT shared proportionaly meaning that if one side gets 30% it doesn't mean that the other side gets 70%. There will be some overlap depending on the load and position. EACH channel A and B need to be characterized independent of one another. BTW) I'm pulling this information from my own personal experience of working Research and Development in the prosthetic industry, where "pendulum" effects of this nature are a real design issue. Studying what the human body already does in relation to opposing muscle groups is a real eye opener.
  • Mark_TMark_T Posts: 1,981
    edited 2014-03-02 03:51
    Ah, I understand now. You need a specialist control system, hydraulic actuators are non-linear and
    a simple PID loop is unlikely to be sufficient, the Project Hexapod folks had a lot of problems with
    closed loop control of a hydraulic robot leg, don't expect this to be easy.

    See from 1:43 in this video - their simulations accounting for the effective backlash of a
    hydraulic system show huge oscillations...
  • T ChapT Chap Posts: 4,223
    edited 2014-03-02 05:44
    Do you have an arm directly attached to the shaft of a rotary hydraulic motor? If so, there will be no way to finesse the movement with that type of arrangement without an amount of complexity(hardware and software). The motor connected to a pulley with some ratio (reduction) will immediately produce positive results. Of course, speed reduction is a cost, but speed reduction IS the solution. You can run a 2x faster motor with a 1:2 pulley output, so the speed is offset. Adjust the steel cable to suit the load requirement, and fragility is not a factor.
  • Kirk FraserKirk Fraser Posts: 364
    edited 2014-03-02 07:11
    Beau, On first look Myography looked weird and complicated but with your second post on it explaining how you used it, it got me thinking of paying attention to how my muscles change over when letting a weight down. I'll think on that more, it seems like a solution is there to be discovered. Thanks.

    Mark, Interesting video. I especially liked the dual pump and the cute accumulators. My accumulators are just long pipes. I hadn't thought about running a simulation. Thanks.

    T Chap, The only advantage I can see for a pulley system is allowing end effectors such as a hand with fingers to be smaller. You still need all of the rest of the system. So at this stage I'm staying simple. Thanks.
  • kwinnkwinn Posts: 8,697
    edited 2014-03-02 11:03
    There is no reason a hydraulic system cannot control the motion of your arm precisely. Instron and other companies have servo hydraulic tensile testers that can apply thousands of pounds of force and control the motion with high precision. They use servo-hydraulic valves and PID control software. Perhaps you should consider a sevo-hydraulic valve for your system so you can control the arm travel in both directions.
  • LawsonLawson Posts: 870
    edited 2014-03-03 09:14
    Assuming that the valve is a simple proportional valve, you're going to have trouble with non-linearities when applying a PID controller. My suggestion would be to fit a differential pressure sensor between the outputs of the proportional valve, and make a very fast inner control loop to regulate the pressure difference seen by the actuator using the proportional valve. This pressure regulator and valve combo then forms a nice (mostly) linear "torque modulator" that a PID control can drive just like an electric motor.

    As for the gravitational torque, that's just geometry. Any good description of a pendulum will walk you through the math. If the mechanical configuration of the arm is predictable, you should be able to calculate the torque needed to balance gravity in real time and simply add that to the output of your PID controller. This will largely remove errors due to gravitational torque from the PID loop.

    Marty

    P.S. a lot of the early industrial robotic arms were hydraulic. So there is a solution.
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