Motorized camera slider - project

[Ajl]

Hello,

I'm new to this forum, and I hope you can help me.

I'm working on a project to build my own motorized camera slider. Before I buy all the components, I want to be sure about my calculations. Mechanical engineering was never my forte, that's why I'm looking for help on this forum.
As you can see in the sketch below, the slider will consist of 2 perpendicular steel shafts, that will carry the weight of sliding dolly (linear bearing + housing), camera and mount. Underneath between the shafts, there will be a timing belt that will be connected to the dolly. One of the pulleys of the timing belt will be connected to a stepper motor with a timing belt of selected transmission.

http://shrani.si/t/2E/XD/1jG1hEmt/1/img001.jpg
- I apologize for the sketch. I'm not really good at drawing.

1) I'm interested in how to determine carrying capacity of the shaft, so I know which one to buy in respect to the selected load. And how to determine what would the deflection of the shaft be, so I can determine the size of supports for the shaft I need.

2) I also want to determine the power and torque needed of a stepper motor.

- How to determine the maximum force acting on the stepper motor. How are the weight force, frictional force, force of static friction and force of acceleration acting in respect to each other. Are there any other forces I forgot to mention? I've chosen the wanted maximum speed, time of acceleration to maximum speed.
- What is the effectiveness of the timing belt, and how to determine what torque is present in pulleys?


I hope that's not too much to ask. I do hope we can find the solutions.


Alan J


P.S.: English is not my mother language, so I apologize for any mistakes.

 

[tygerdawg]

You said "perpendicular" I assume you actually meant to say "parallel".

The loading of the rails is a beam bending stress problem. You'd have to run through those calculations...if you wanted to. The first step would be to determine your load. How much does your camera weigh?

You could probably save yourself a lot of trouble just purchasing something suitable from a catalog. Here is one company www.pbclinear.com that I have used before. They have very good PDF catalogs with useful sections on Engineering.

Sizing a stepper motor is all about providing enough torque for the peak (or max) torque your application will require. Peak torque is the max combination of all the torques: acceleration torque required to move your mass up to desired speed, torque to overcome gravity, friction & stiction torque, others...try to account for everything. Torques for rotational component angular acceleration & linear component translational accelerations. You must determine your desired speed, and how fast you want to achieve that speed. That is the basis for almost everything about sizing the motor. Then multiple by a suitable safety factor. Oversize it: torque is cheap, buy plenty of it. Websearch for "Smart Motion Cheat Sheet" and get a quick tutorial on dynamics calculations. My favorite stepper motors are from www.imshome.com .

 

[Ajl]

Hello,

I thank you for your reply.

Yes, what I meant was "parallel". I tried to edit and correct it in the original post, but I couldn't find the edit option.

As I like to learn new things every day, I've chosen to approach the "harder" - calculation way, to solve the problem.

I will mainly use the slider for a GoPro camera, but as I want to broaden the usage of the slider, I've looked up on the internet, which DSLR cameras and lenses are best selling. Next I've selected the camera body and camera lens with the highest mass/length.

What I'm curious now is this. Which camera/lens position will generate the highest stress on the shaft. In the attachment bellow I assumed, one of the two depicted camera positions will generate the stress I'm looking for.

http://shrani.si/t/2K/SO/14acFodb/2/img002.jpg

Is the simplified version of the in position 1. drawn correct? How to determine the forces Fay,Fby,Fbx? Is there force and momentum acting under the camera mount?

I thank you for your time and answers.Alan J

P.S.: I've disregarded the weights of plate + bearings with housing, because of their little mass.

 

[tygerdawg]

This is a classic "statics" problem in engineering mechanics.
Resolve all forces to a desired coordinate system (as you have done).
Sum the forces all acting in the same direction.
Calculate the torques ("moments") around your axes.

These establish your loading conditions on your rails.
Your camera + lens will sum the total weight load of both. The offset lens will produce a torque around the mounting plate. And so on.

 

[Ajl]

Hello,

I thank you for your reply and your help.

I have done the calculations on problems I mentioned and depicted in my previous post. Would anyone be so kind to check if these are correct?
-----------------------------------------------------------------------------------------------
Calculation - 1
http://shrani.si/t/26/E/1cItmvPq/izracun-obrem-1.jpg

Calculation - 2
http://shrani.si/t/2d/mj/3eBVHoSF/izracun-obrem-2.jpg
"Fay" in this position would not exert any force on shaft. This force would be countered entirely by timing belt (stepper motor)
-----------------------------------------------------------------------------------------------
If these values are OK, how do I approach the problem next? Should I calculate the maximum bending stress, that the biggest calculated value exerts in the middle of my shaft? I would assume, that value would be "Fby" from calculation no.1, correct?

I thank you for your time and answers.


Alan J

 

[nvn]

Ajl: Yes, your simplified versions currently seem to be drawn correctly. In post 5, calculation pages 1 and 2 look correct, except I think 1,383 on page 1 perhaps should be 1,381 250, which changes 28,24 N.

Should I calculate the maximum bending stress, which the biggest calculated value exerts in the middle of my shaft? I would assume, that value would be Fby from calculation no. 1, correct?

Yes, that is correct.

 

[Ajl]

Hello,

Thank you for your answer.

I'm trying to size my shaft now (diameter). How much can a shaft bend, for the bearings that run over it not to get stuck?Alan J

 

[nvn]

Ajl: Unless your particular bearing specification states otherwise, I currently would guess your bearings might get stuck if K exceeds 0,000 500 rad/mm, where K = 0,25*P*L/(E*I), P = shaft transverse applied force (such as Fby in your calculation page 1), L = shaft length, E = shaft modulus of elasticity, and I = shaft second moment of area.

 

[Patricio1976]

I´m making a similar project. We can exchange experience. Take a look here: http://timeblocks.wordpress.com/