Motion Calculations


Thread Starter


Can anyone suggest a good reference book(s) that can aid in motion calculations?

I am in the process of designing a system of five belts that takes in small plastic packets filled with liquid shampoo. Above each of the five belts is a photoelectric sensor. Once a packet reaches belt number five, belt number five is suppose to feed each packet onto a different
belt (running at a fixed speed) on another machine. The target belt has lugs on it. I need to get my shampoo packets between the two lugs on the target belt.

Needless to say, I am pulling out my hair! Can anyone suggest a good reference to get me going?
Money is tight (as always). It seems simple enough, but I am having trouble on how I am going to calculate speeds at which I can hit my target.


Thank you in advance!

Cameron Anderson

I have not really seen any good books out there (of course I haven't looked very hard). I am working on my own handbook for sizing different mechanical system, motion profiles, thrust, torque...etc. I was suppose to have it done on the 4th...but have been too busy with applications. Here are basic formulas for calculating Average and Max Velocity, and Max acceleration.

Triangular profile:
(1/2 time accelerating, 1/2 time decelerating)

Vmax = (2 x d)/t
Vavg = d / t
Amax = (4 x d)/t^2

1/3 Trap profile:
(1/3 time accel, 1/3 time at speed, 1/3 decel)

Vmax = (1.5 x d)/t
Vavg = d / t
Amax = (4.5 x d)/t^2

d = distance
t = time
V = velocity

Torque Calculations:
Torque = Inertia x Rotational Acceleration
T = J x a
Tpeak = Trl + (Jt x a)/e

Bill Rosser - UCS

I do not know if it will help, but I have a number of in-motion weight controller manuals from UNIPULSE that provide some pretty good
background formulas for Belt Scales, in-line checkweighers, and axle scales. The formula calculations might help.

I would be happy to send you a CD with the manuals on PDF files if I could get your address.
(the in-line checkweigher manual is about 120 pages)

Cameron Anderson

I noticed that only 1/3 of my post is actually there....if you want the rest of the formula's...let me know.

Cameron Anderson
"Control System Design Guide" by George Ellis.

Don't pull your hair too much as you won't have any use for all that shampoo.
If it's simply a matter of feeding between the lugs, I might be inclined to simply put a cam on the fixed speed belt that gave me a "feed window" signal. Advance belt 5 into the "about to feed" position, and wait for the feed window signal, or if it's already on, continue to feed the packet.

This cam to be set on at the earliest point you can feed the packet with the lead edge hitting the first lug, going off at the last point you can feed the packet and be ahead of the second lug.


Christopher Brehm

I have done many calculations and programs that do what you are talking about (placement of an object on fixed speed belt). I've also done
placement of objects on belts that are accelerating / decelerating, calculations for jerk (acceleration of acceleration) for such a purpose (useful if container has a liquid that will spill if too much jerk is applied), etc.

If you still have not figured out how to do this send me an email.

In short, when feeding a fixed speed conveyor the time it takes the shampoo bottle to reach reference point is known. You can use fixed
acceleration (easiest for calcs) and determine from this time how long you need to accel/decel before shampoo bottle gets to the fixed speed

Good Luck,

Christopher Brehm
[email protected]