## Simple Motion Calculations

## Simple Motion Calculations

(OP)

This is a simple spreadsheet to manipulate four physical quantities associated with motion calculations: position (x); its first derivative, velocity (v); its second derivative, acceleration (a), and of course, time (t). These quantities are related by several familiar equations, which can in turn be expanded by substitution to cover any combination. The spreadsheet is protected without a password to avoid inadvertent destruction of the formulas. Keep units consistent.

## RE: Simple Motion Calculations

I use these equations when doing tech support when the customer says he wants to move a distance in so much time. I can quickly calculate the velocity and average acceleration.

v=1.5*∆s/∆t

a=4.5*∆s/∆t

^{2}These equations that the acceleration and deceleration ramp are 1/4 of the total distance, ∆s and that acceleration and deceleration ramp times are about 1/3 the total movement time, ∆t. These equations assume the motion profile uses linear ramps. However, most motion controllers use s curves so there are modifiers to use the average acceleration/deceleration to calculate the peak values.

3rd order s curves 2.0 x average acceleration or deceleration

5th order s curves 1.5

7th order s curves 1.875

cosine s curves 1.57 or PI/2

I have memorized so I can quickly bang out estimates on a calculator when talking on the phone.

## RE: Simple Motion Calculations

I'm not sure if the spread sheet can be modified after posting. Does anyone know? I have attached a spread sheet that addresses the "travel" portion of the velocity profile. I'm not sure where I downloaded this from, so if you recognize it please give or take credit.

## RE: Simple Motion Calculations

This one needs some improvement. This shows how one can generate 3rd order motion profiles using symbolic processing. I used wxMaxima to generate the html. If you have wxMaxima installed you can just cut, paste and run the code.

Try doing this in a spread sheet:

ftp://

You need to wait a while for the images to download at the bottom of the file. If you have your own website then you can easily add html files to it.

wxMaxima is not perfect but it is free and can do most math required to generate motion profiles.

## RE: Simple Motion Calculations

thread404-238396: Linear Motion equations for trapezoidal move

PNachtwey,

I'm afraid that I'm not in a position to have my own FTP site, nor am I able to take advantage of the software you suggest (Scilab & wxMaxima). Maybe some day, sounds interesting. .

## RE: Simple Motion Calculations

wxMaxima and Scilab are free.

PLC people may use linear ramps but motion control people normally use s curves. 3rd order profiles are the lowest order to provide s curves.

## RE: Simple Motion Calculations

My willingness to embrace your suggestions about free software and ease of distribution is not the problem. "IT" is the problem. And I know it's hard to believe, I do not have personal access to the internet. Alas, I must live within the guidelines established by the all wise "IT" department. As for your comments about motion control, I think you have a lot to contribute and look forward to your participation.

## RE: Simple Motion Calculations

## RE: Simple Motion Calculations

Well said. I'm off to set them (IT) straight!