Unable to decide motor spec for Quadruped

[saba_rish91]

Hello,

I am planning to build a quadruped robot and I am not good with robot mechanics.

The body of the robot is going to contain Arduino UNO, servo controller and LiPO battery. I'm planning to make the robot's body with acrylic sheet and the leg joints using Aluminum metal. Each leg with 3 DOF.

I'm unable to decide the servo motor's torque required to make the robot walk on a smooth surface and on slightly uneven surface.

Which of the following servo motors can achieve this task?

http://robokits.co.in/shop/index.php?main_page=product_info&cPath=2_5&products_id=187
or
HiTec HS 311?

Thanks in advance.

[waltr]

How much does the Bot weigh?
How many servos will support the bot with the minimum number of legs on the ground?
What are the moment arm lengths connect to the servos? Remember how Torque is defined (T = Force times Arm length).

[jwatte]

With 2DOF, you can actually use fairly weak servos. The reason is that the force goes straight into the mounts and axles of the servos, rather than actually in the motor radial direction. Once you add a third degree of freedom, that will have to lift some part of the robot, and the leg.

It's not so bad. Simplified math that works OK: If you assume that the other legs are already holding the main body, then the middle (knee) joint only needs to lift the weight of the leg outside the joint, times the horizontal distance between the servo spline (center of rotation) and the center of gravity of that leg.
For the other three servos to keep the body still, they need to lift one-third of the weight of the entire robot, times the distance between the center of rotation of the joint and the center of gravity of "their third" (which can be approximated as half of the distance between the center of rotation and the center of the robot.)

As you know, torque is simply weight, times distance to center of mass.

Now, add a 50-100% safety margin, and you're likely good to go!

[saba_rish91]

With 2DOF, you can actually use fairly weak servos. The reason is that the force goes straight into the mounts and axles of the servos, rather than actually in the motor radial direction. Once you add a third degree of freedom, that will have to lift some part of the robot, and the leg.

It's not so bad. Simplified math that works OK: If you assume that the other legs are already holding the main body, then the middle (knee) joint only needs to lift the weight of the leg outside the joint, times the horizontal distance between the servo spline (center of rotation) and the center of gravity of that leg.
For the other three servos to keep the body still, they need to lift one-third of the weight of the entire robot, times the distance between the center of rotation of the joint and the center of gravity of "their third" (which can be approximated as half of the distance between the center of rotation and the center of the robot.)

As you know, torque is simply weight, times distance to center of mass.

Now, add a 50-100% safety margin, and you're likely good to go!

Suppose my bot is around 1Kg (I think it won't weigh that much). The hip motors just require to move the leg right? A leg might weigh around 190gm (2*45gm+100gm). Then, a low torque motor might be sufficient.
I think the Knee (servo closet to ground) servo requires the maximum torque. If the distance between the knee servo and the hip servo is 9cm. Distance between the hip servo and the center of gravity be 3cm. Then is the torque required is really 12Kgcm? or it is  (1/3)*12=4Kg-cm?

[jwatte]

In this diagram, the servo at A only moves the orange piece ("foot") left or right, and the distance part of distance-times-weight is almost zero. Thus, very little torque is actually needed.

The servo at C is mounted to move the legs horizontally (hither or yon, into or out of the drawing) and there is no real load in that direction, thus that servo also needs very little torque.

Remains servo at B, the "knee" servo. When the rest of the body is still, it lifts the orange and green pieces, as well as the servo A itself. The center of gravity is probably somewhere towards the end of the green piece and a bit down. The horizontal distance from COG to the servo is thus shorter than the green piece. The torque needed for this lifting is weight of green plus orange plus servo A, times approximately two thirds the length of the green piece.

Now, the other servos in position B, on the other legs, keeping the body up, are each lifting 1/3 of the weight of blue leg pieces plus purple body plus servo C. This is assuming each of the legs (green + orange) are fixed, in contact with the ground. Each of them see a center of gravity approximately at servo C (depending on weight distribution between purple and blue, could be closer.) This may be a bit bigger than a servo B sees when it's lifting the outer limb part.

And this is simplified -- I'm not a mechanical engineer, so the statics and dynamics math for the actual solution isn't something I know how to solve, but this "rough estimate" works for several others that have done walkers, so I believe it :-)

So, torque for servo B is the maximum of either:
weight(green + A + orange) * length(2/3 of green)
weight(4/3 * blue + 4/3 * C + 1/2 * purple) * length(blue)

If you lift two legs at a time, crosswise, then the second term becomes:
weight(2 * blue + 2 * C + 1/2 * purple) * length(blue)

And, again, add a 60-100% safety margin.
All distances are measured horizontally only (projected to the plane perpendicular to gravity, if you're good with 3D geometry.)

[saba_rish91]

@jwatte Thanks a lot.

I was browsing through internet and I found the following site on hexabot's mechanics.

http://www.robotshop.com/robot-leg-tutorial.html

In that site, it says that the servomotor near to the ground requires more torque compared to the middle servomotor!

[saba_rish91]

Also, is there ay software which lets us to test robots virtually?

[jwatte]

@jwatte Thanks a lot.

I was browsing through internet and I found the following site on hexabot's mechanics.

http://www.robotshop.com/robot-leg-tutorial.html

In that site, it says that the servomotor near to the ground requires more torque compared to the middle servomotor!

I suppose by "near to the ground" you mean servo A in this diagram. The question is one of statics/dynamics. Most of the force of the servo A is taken by the bearings of the servo, rather than the servo motor itself, because the foot is pointing straight down. This is not the case for the servo B -- it is close to pessimal in this regard.

[waltr]

@jwatte Thanks a lot.

I was browsing through internet and I found the following site on hexabot's mechanics.

http://www.robotshop.com/robot-leg-tutorial.html

In that site, it says that the servomotor near to the ground requires more torque compared to the middle servomotor!

I suppose by "near to the ground" you mean servo A in this diagram. The question is one of statics/dynamics. Most of the force of the servo A is taken by the bearings of the servo, rather than the servo motor itself, because the foot is pointing straight down. This is not the case for the servo B -- it is close to pessimal in this regard.

If the joint at A has a horizontal pivot then the level arm is the distance from the pivot at A the the body of the Bot at point C. Therefore this servo would require the greatest amount of torque on hold the bot's body off the ground.

[jwatte]

If the joint at A has a horizontal pivot then the level arm is the distance from the pivot at A the the body of the Bot at point C. Therefore this servo would require the greatest amount of torque on hold the bot's body off the ground.

I thought so too for a long time! But, it turns out, if the rest of the robot is rigid, then that's not actually the case. Assuming servos B and C can keep the body rigid, A will not see much torque at all.

Consider putting four flat sticks on the ground. Now, put a flat plate on each of those sticks in the corners. (Like a table on table legs.) The table/plate will sit still just fine. If there were any sideways torque on the sticks, they would collapse inwards, but BECAUSE THE PLATE IS RIGID, this does not happen; the sticks simply see downward weight without any torque.