Mechanical Design Assistance???

Rick, the relationship for rotations, or revolutions is gear ratio. For example, if you want 4 rotations of your cultivator per day that means you want ONE rotation every SIX hours, 1/2 rotation every 3 hours or 1/4 rotation every 1.5 hours. Normally you would want a gear ratio between your cultivator base size and your motors pulley size. However, since you're going to use stepper motors,  all you should need to do software-wise is make use of timing parameters to step the turntable once every 6 hours. Using wait, if/the, for, or pause commands or some other variable to reference the passing of time should work for you. For example is you want it to turn 1/4 turn, have it 'sleep for 5400 seconds (3600 secs/hr * 1.5 hrs=5400 seconds). Do that 16 times via an "if' or "while' type statements and your turntable will rotate 4 times in a 24 hour period. It's all about the math!

Thanks for the info Michael...

I think I have it worked out now. The control application will just be a simple state machine based on "the big loop". Reading sensors, performing control functions and logging them, via the radio, back to the central control/monitor system. I think control functions and reading the sensors should be very lightweight. There's no sensor that needs to be read more than once a second, and that's probably overkill. As the EZR32WG has some very low power modes available I plan to have it sleep most of the time and wake up only periodically to run the loop. The central control/monitor will have the ability to wake the crowing area system up at any time and instruct it to read sensors and/or perform control functions.

I'll have to workout all the timing and pulse count once I have the MCU in hand and the rotator is completed. So far my calculations go like this... My stepper motor is geared and requires 4096 pulses per revolution. There is about a 10:1 ration between the timing gear, at the turntable, and timing pulley on the stepper motor. That gives me about 41,000 pulses per revolution at the turntable. If I want 4 revolutions per day so that's 164,000 pulses per day. That works out to about 2 pulses per second. So I could just pulse it a couple of times on each wake up cycle. Since the motor is geared it doesn't require power to remain stationary. We'll see.

Right now I'm waiting on the final parts for the turntable and on the E14 kit. It's all just theory right now. lol...

RWReynolds

It looks like your design is coming together.

Two comments.

The stepper I linked to, Terry made this comment.

This means your pulse number might be lower. (half)

With the geared output you already have increased the step angle by 64, so you don't require 8 steps ...

The output angle per pulse is close to 0.178 deg.

balearicdynamics Enrico's idea for the tensioner is a good one.

You could mount your stepper and drive wheel on plate that pivots at one end, and has a spring pulling it onto the disc.

If the length was long, it would allow for a few millimeters vertical movement at the drive cog.

If you ensure the belt is wider than the base, you could add a disc onto the top and bottom of the drive cog to ensures it stays in contact with the belt.

This would allow for any wobble your large disc has.

Mark

RWReynolds

It looks like your design is coming together.

Two comments.

The stepper I linked to, Terry made this comment.

This means your pulse number might be lower. (half)

With the geared output you already have increased the step angle by 64, so you don't require 8 steps ...

The output angle per pulse is close to 0.178 deg.

balearicdynamics Enrico's idea for the tensioner is a good one.

You could mount your stepper and drive wheel on plate that pivots at one end, and has a spring pulling it onto the disc.

If the length was long, it would allow for a few millimeters vertical movement at the drive cog.

If you ensure the belt is wider than the base, you could add a disc onto the top and bottom of the drive cog to ensures it stays in contact with the belt.

This would allow for any wobble your large disc has.

Mark

Thanks for the info mcb1.

I will take into account the info on the steps per revolution. On one of the sites where I researched the motor it did say 4096. I will have it connected soon to a Raspberry Pi for testing. Then I can work out the exact pulse count and timing required.

I was planning to mount the motor in such a fashion as to allow for some spring tensioning against the timing gear. I just have to work out the mount now.

Cheers,

Rick

Fist post here. I hope it's ok to continue on an old thread - there are some similarities to my current project.

It's a long time since I attempted any angular motion calculations - so please forgive any obvious mistakes...I have ignored friction below on the assumption it will be negligible compared to torque/power required for acceleration (not sure if that is wise though).

I'd like to use a stepper (or steppers if needed) to rotate a plywood disk (with a person standing on top) of 1200 mm dia 30° in 1.25 secs. The timing belt drive disk will be 1160 mm dia as the centre of a 1200/1160/1200 mm sandwich with a lazy susan on the bottom. I plan to use something like the AccelStepper library (not sure if providing a link to that is ok?) to do:

1. from rest provide constant acceleration for 0.5 secs
2. constant angular velocity for 0.25 secs
3. const decelerate for 0.5 secs to rest

I calculated the approximate moment of inertia (plywood + person as 100 kg point load on perimeter of disc) as 39.16kgm²

Torque/Power Calculation:

Say, use Accelstepper Library to apply the above:

(i) constant acceleration, α, (from 0 rad/s) for 10° to maximum ω rad/s. Say time taken = 0.5 secs

(ii) zero acceleration for 10° to 20°. Say time taken = 0.25 secs

(iii) constant deceleration , α,  from 20° to 30° for 10° (from  ω rad/s to 0 rad/s). Say time taken = 0.5 secs

i.e. total time taken is 1.25 secs for 30° start-to-stop

Considering only item (i) for now:

Angular Displacement, θ = 10° (or  0.1746 rads)

For rotational motion with constant Angular Acceleration:

θ = (1/2)(ω₀ + ω)t

since ω₀ = 0 rad/s

0.1746 = 0.5 (0 + ω) 0.5 -> ω = 0.1746 / 0.25 -> ω = 0.6984 rad/s

α = (ω - ω₀)/t -> α = (0.6984 - 0)/0.5 -> α = 1.3968 rad.sec^-2

Torque required to produce this stated radial acceleration:

τ = Iα -> τ = 39.16 x 1.3968 Nm -> τ =  54.7 Nm (Max)

Force required to produce this Torque:

τ = Fd so F = τ / d

"d" for the disk with the glued on timing belt is = 1160mm/2 = 0.58m

therefore

F = τ / d -> F = 54.7 / 0.58 -> F = 94.31 N

Work done by torque τ is W = τ x θ

Power, P = d/dt(W) = d/dt( τ x θ ) = τ x dθ/dt

since ω = dθ/dt

Power = τ x ω

Power = 54.7 x 0.6984 -> Power = 38.2 Watts (Max)

Question(s):

I have a rough idea how a stepper works but i'm not really sure how to specify a particular stepper/gearing ratio to "make this happen" - any ideas along that route would be most appreciated (based on quoted power alone I have a feeling I may need 2 x Nema 42!!).

Other:

of related interest - using an 80MHz processor (compared to a 16MHz Arduino Uno) increases the Accelstepper acceleration 5 fold e.g. https://www.youtube.com/watch?v=Hsl3dbRPLTw

...that e.g. used a bipolar nema 34 at 1.8°/step (200steps/rev)

Hi Andrew,

Your person standing on the turntable makes any specific calculation of the torques involved very difficult. The structure of the human body will absorb the movement and only follow a 1.5 second rotation in an elastic manner. To smooth out the rotation I would consider 15 degrees of acceleration and 15 degrees of deceleration. This will slightly improve the amount of torque needed and should improve the overall feel of the rotation to the subject. Foot position of the subject on the disk should not affect overall torque but an imbalance of weight distribution may make friction in the bearings a factor that needs to be considered. Foot position may also affect the amount of elasticity in the bones and muscles of the body and hence change the dynamics of the rotation. By over engineering the problem you should be able to make it work.

John

Much appreciated John - food for thought. I guess the proof of the pudding is...that it wobbles . Much experimenting & various poses required - neither is the 1.5 secs set in stone.

I had imagined the 100Kg load / position as the over-engineered extreme (I should have mentioned that though).

"15 degrees of acceleration and 15 degrees of deceleration"

I'd prefer something approaching a sinusoid (i.e. zero, slight +ve, large +ve, slight +ve, zero, slight -ve , large -ve, slight -ve, zero) for the acceleration profile but I haven't looked in detail whether that can be approximated by a series of steps through the AccelStepper library yet.

To be honest I have practically zero mechanical design experience and i'm probably hoping for further comment re how to identify a suitable stepper and how to size the pulley and belt pitch gearing relationship...

Thanks,

Andrew.

Edit:

Having reviewed the "trapezoidal velocity profile" produced by the the positive accel pulse / zero accel / negative accel pulse i'm no longer sure the sinusoid accel profile I had referred to would be any better than this:

As jw0752 said the postion could affect the friction.

As a cheap source you may wish to consider using automotive components.

Either the rear or front hub turned on its side, would easily cater for uneven loading while retaining the same friction.

Depending on what option you choose the drive axle could be retained to allow different options to drive it.

Looks like an exciting project.

Good luck

Mark

Hi Andrew,

The reason I suggested a steadily accelerating and decelerating program is that for any time frame it will have the lowest dv/dt. Any time spent at constant velocity is a waste and only creates the need for higher torques and higher accelerations at the beginning and ends of the cycle.

John

I'll keep that in mind Mark - at the minute I have one eye on keeping the solution mobile (and weight down) so will try the lazy susan and some roller bearings around the perimeter first.

Understood John - while that will keep torque down i'm equally concerned about the effect (on the  person) of the sudden change from +ve accel to -ve accel (not mitigated by the period of zero accel). Of course, the fact the shorter periods of accel/decel must be harsher may offset the benefit I refer to...perhaps a short period of zero accel will help.

We'll see!

Thanks,

Andrew.

Well, I received my 390mm dia lazy-susan a while back (image attached) but it'll sit in a corner some more yet.

Reading lots that I hadn't been aware of e.g "inertia-matching" it seems direct-coupling of gearhead/stepper to the turntable may be preferable (neither had I been fully aware of the reduction in reflected load inertia by the square of the gearbox ratio).

While a direct coupling scenario does work around some complexity (belt-drive redundancy / no requirement for circular ply) I can't say that the lazy-susan bearing is the most accurate "circle" i've ever come across (the bearing is a little sticky at a point to rotate by hand).

Perhaps the accuracy that would be required via a direct coupling from the gearhead output to the underside of the plywood make this newly conceived contrivance impractical?

If someone where to comment on this point it would be useful. However, if the idea where seen as potentially practical then any hint to the nature (by example) of a gearhead shaft to underside of plywood "coupler" would be appreciated as I have very little idea what that could be.

Andrew.

Hi John - I see you are still in touch with the thread

I had initially included the following link (in my post above) as an example of what rate of change of acceleration could "look like" wrt the the human body (jelly) but had then deleted it.

In case you missed it i'm sure you'll find the re-instated link interesting https://www.youtube.com/watch?v=X4X_EUxqKEo&feature=relmfu

Andrew.

Edit:

for the record, I currently understand step changes in d/dt(Acceleration) to be referred to as "jerk".

Hi Andrew,

Thanks for the link. It is quite impressive to see the difference between the steady and contoured acceleration rates. This is a good example of how interesting things can get when we take the time to dig deeper into the physics. I saw your first post as it came through on my e-mail notice but then I couldn't find it on your E-14 posting so I assumed that you edited it off. Thanks for reposting as I am sure others will find it interesting too.

John