2

### Author Topic: Calculating torque for cylincrical robot arm  (Read 7235 times)

0 Members and 1 Guest are viewing this topic.

#### kennykck

• Jr. Member
• Posts: 43
##### Calculating torque for cylincrical robot arm
« on: November 26, 2007, 08:31:24 AM »
Hi,currently i'm building a cylindrical robot arm which has 4 axis( translational and rotational motion in both X and Z axis)
Let's say i placed a motor at the base to rotate the arm in z axis. How do i calculate the torque needed to rotate the arm horizontally? The only requirement i have is to rotate the arm horizontally in 4 seconds in one full circle.

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #1 on: November 26, 2007, 09:31:03 AM »
I'm not sure how you defined each axis and which joints you want calculated.

Can you draw me a free body diagram (FBD) of the arm?

Something like this, with your axes labeled:

Quote
How do i calculate the torque needed to rotate the arm horizontally? The only requirement i have is to rotate the arm horizontally in 4 seconds in one full circle.
Horizontally . . . assuming friction is zero . . . so you need to factor in rotational momentum.

Basically its acceleration of a mass about a point, similar to what you learn in physics (swinging a ball tied to a string, etc.). So you want to know the torque required to accelerate a mass at X length to travel 360 degrees in Y time?

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #2 on: November 26, 2007, 10:00:14 AM »

Horizontally . . . assuming friction is zero . . . so you need to factor in rotational momentum.

Basically its acceleration of a mass about a point, similar to what you learn in physics (swinging a ball tied to a string, etc.). So you want to know the torque required to accelerate a mass at X length to travel 360 degrees in Y time?

I hope my drawing can eliminate the confusion.

Yes, i want to know what u just mention up there.

I had been studying about, Torque = moment of inertia * angular acceleration.
I'm not sure whether i should be using this formula or not. But this formula really giving me headache. So I hope u can give me some guide.

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #3 on: November 26, 2007, 10:16:22 AM »
Take your equation and break it up into sub components:

Torque = moment of inertia * angular acceleration

torque = (mass * distance^2) * (change_in_angle / change_in_time)

(i think you can figure it out from there)

where distance is defined as the distance from the rotation axis to the center of mass of the arm:
center of mass of the arm = distance = 1/2 * (arm_length)
(use arm mass)

but you also need to account for the object your arm holds:
center of mass of the arm = distance = arm_length
(use object mass)

so calculate torque for both the arm and then again for the object, then add the two torques together for the total

if you put all this in excel, you can easily change values to see how different factors affect torque

maybe useful for you:
http://en.wikipedia.org/wiki/Angular_acceleration
http://en.wikipedia.org/wiki/Moment_of_inertia

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #4 on: November 26, 2007, 11:17:30 AM »
I think the method u suggest is valid only for calculating a point of mass, is it?
Because i saw a book the formula to calculate the moment of inertia for rectangular block is given by formula

I = (1/12)*m(a^2 + l^2)

Since I'm using hollow beam as my robot arm, I had to divide the beam into 4 rectangular block in order to calculate. Then I used Parallel axis theorem(from wiki) to find the moment of inertia for the beam rotating in the Z axis ( my horizontal beam does not pass through the Z axis). And then I proceed in calculating my vertical beam. My problem arise when i need to include the moment of inertia of motors, load, etc. Way too many things to calculate... before i can comes up with the total moment of inertia. Not sure if i'm doing right this way.

Also, since my requirement is only 4 sec in rotating in a circle, how do i get the angular acceleration, angular velocity, angle travel? Can i just assume my angular acceleration is 1sec, angular velocity is 2 sec, and angular deceleration is 1 sec(total 4 sec). I hope u can understand my drawing. Really need your help. Thanks.

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #5 on: November 26, 2007, 12:32:20 PM »
How exact of a solution do you need?

In terms of building the arm, the equations I gave you are sufficient.

I say this because as you said, there are quite a lot of details. The point mass assumption will get you within a few percent of the correct answer.

Plus, your equations don't account for things like friction, air resistance, gear inefficiency, etc.

And also remember that your robot will be lifting a large variety of objects at numerous orientations, so in the end you will still need to estimate . . .

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #6 on: November 26, 2007, 09:04:06 PM »
Since i'm doing my final year thesis (degree) in this robot arm, the point mass method you given me, is it sufficient enough for my thesis report? (for calculating the motor torque requirement)

Say my mass of whole arm is 12.7kg, the distance of my center of gravity(arm) from the z axis rotation is 0.52m.
assume my acceleration time is 1sec, changes in angle is 90 degree(equals to pi/2).

torque = (mass * distance^2) * (change_in_angle / change_in_time)

I should get torque = 5.394 Nm. (I'll add in the load and 20% extra later)

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #7 on: November 26, 2007, 09:29:57 PM »
Quote
Since i'm doing my final year thesis (degree) in this robot arm, the point mass method you given me, is it sufficient enough for my thesis report?

If you just need this torque information to build the robot and nothing else, I'd bet my degree in mechanical engineering that this is good enough

If you want to do it the correct notational way, get a book on robotic manipulation basics and look up something called a Jacobian, a 'matrix entity' used to study both static forces and velocities. At least thats what my book says (yea, you made me break my old books out the closet! ).

Personally I think its just overcomplicated math thats only good for control theory and not mechanical design . . .

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #8 on: November 26, 2007, 09:38:46 PM »
Thank you very much!

I only need the torque data so i can purchase suitable motor for my prototype, at the same time acceptable in thesis report wiring.

I had to say this is the best robotic forum i'd come across so far.

Many thanks.

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #9 on: January 04, 2008, 08:35:04 AM »
Now I wanna do dynamic calculation for my robot. So what are the things that i should calculate? Vibration and friction is out of my study. Thanks for replying.

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #10 on: January 04, 2008, 08:42:11 AM »
Not sure if you noticed or not, but because of your post I added dynamics to the robot arm calculator

Hopefully it will save you time . . .

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #11 on: January 04, 2008, 11:20:29 AM »
Did u mean the Joint Rotational Velocities?

Anyway, in terms of design of mechanical structure for my robot, i had done the moment & force calculation; torque requirement for a given velocity and time(for motor selection); what else should i do?

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #12 on: January 04, 2008, 12:32:45 PM »
In terms of motor selection you are ok with what you got.

Did you calculate for sagging? Meaning if you have the arm stretched out carrying some heavy weight, do you know how much it sags? Its a bit complicated at first, but look up stress analysis basics.

You might also want to calculate both the forward and inverse kinematics, too.

Then you want to calculate how much power each actuator will draw so you can select your power source/system.

#### kennykck

• Jr. Member
• Posts: 43
##### Re: Calculating torque for cylincrical robot arm
« Reply #13 on: January 05, 2008, 01:52:21 AM »
In terms of motor selection you are ok with what you got.

Did you calculate for sagging? Meaning if you have the arm stretched out carrying some heavy weight, do you know how much it sags? Its a bit complicated at first, but look up stress analysis basics.

You might also want to calculate both the forward and inverse kinematics, too.

Then you want to calculate how much power each actuator will draw so you can select your power source/system.

I have done the FEA simulation to find the stress endures and sagging displacement in static condition. I'll do forward and inverse kinematics as well.

I'm designing for high speed robot arm. If my arm accelerate and decelerate very fast, it'll cause the vertical beam to deflect a bit when it stops, isnt it. So should i calculate the force that cause the deflection due to the dynamic motion.

Also, since this is my thesis project, i wanna ask your opinion first whether all this work is enough for a thesis? What kind of problem my robot will face during motion that i should calculate/study? I'm quite blank now...

• Supreme Robot
• Posts: 11,680
##### Re: Calculating torque for cylincrical robot arm
« Reply #14 on: January 05, 2008, 09:11:20 AM »
Quote
I'm designing for high speed robot arm. If my arm accelerate and decelerate very fast, it'll cause the vertical beam to deflect a bit when it stops, isnt it. So should i calculate the force that cause the deflection due to the dynamic motion.
Well . . . I dont think you need to, unless you plan for the arm to grab something while its moving . . . there comes a point where you can say you over designed it . . .

Quote
Also, since this is my thesis project, i wanna ask your opinion first whether all this work is enough for a thesis? What kind of problem my robot will face during motion that i should calculate/study? I'm quite blank now...
Well, the point of a thesis is just like writing a paper - to discover and prove new science. Building a robot arm isn't new science, unless you have some theory that you want to prove with the arm.

For example, I am doing work on a robot fish fin. No one really understood how fish fins work, so I built a robot version, attached force sensors to it, then used it to discover how the fin worked.

You building a robot arm is only the first part of your project, really.