hi… ur tutorial was very useful. i was wondering if u could provide a similar tutorial for a humanoid robots leg torque calculation (bipedal walking movements).
Thank you
Hi, I use the equations above but there is a problem. Torques never changes when I change the robot weight. Can the torques be independent from robot weight?
The weight of the robot has a direct correlation to the torque required by each joint. If you can spot an error in the equations, we are more than happy to take a look.
Hey, I;m working on designing a hexapod and stumbled upon these majestic equations! Thank you so much! I was just wondering where the part of 6*(W1+W2+W3) comes from, with emphasis on the six times
@Nick The total weight of the robot involves the weight of the center (W4), plus the weight of the six legs. The weight of a leg comes primarily from the actuators, which are not assumed to all be equal (W1, W2 and W3). When a robot is walking in a tripod gait, only three legs are supporting the weight of the body and all six legs. It is a bit of a simplified model, but it does the trick.
This tutorial is simple and complete. Thanks!
I was wondering about a passage, it’s just curiosity but it would be helpful if you could answer.
When we calculate the weight of the robot (W4) we add the weight of three legs (W_3legs) wich I assume are the raised ones.
In the next equation we find the sum of the reaction forces adding to W4 the weight of the actuators 6(W1 + W2 + W3) of all six legs.
So here’s the question:
- If we assume that a leg’s weight is equal to it’s actuators “(W1 + W2 + W3)”, then why do we count “W_3legs"? Aren’t they alredy considered in "6(W1 + W2 + W3)”? don’t we count three more legs like this?
- If instead we assume that a leg’s weight is equal to “W_leg + (W1 + W2 + W3)”, then why don’t we consider a “W_6*legs” in the W4 equation? don’t we miss part of the weight of the three ground legs?
Hope i didn’t say nothing (too) stupid. Bye!
@Gulferamus
Q1 If we assume that a leg’s weight is equal to its actuators “(W1 + W2 + W3)”, then why do we count “W_3legs”? Aren’t they already considered in “6(W1 + W2 + W3)”? don’t we count three more legs like this?
You are entirely correct. The equation should not include 6*(W1 + W2 + W3)
Q2 If instead we assume that a leg’s weight is equal to “W_leg + (W1 + W2 + W3)”, then why don’t we consider a “W_6*legs” in the W4 equation? don’t we miss part of the weight of the three ground legs?
Correct again - we’ll update the equations as soon as we can and thank you for bringing this to our attention.
what is the value of the t5?
in the torque balance equation for left shoulder what will be the unknown values and what will be the known values… pls explain thank u
@rathan The values will depend on the angle of the actual position of the robot. You need to fill all the values in the equation with your robot par lengths and angles, there is not a single fixed value.
@rathan As mention in the other reply, the value of T5 will vary according to the robot parameters and the angle of the legs. This is not a single value. You need to fill the formula with your parameters ( lengths, angle).
Hi! I have a question on the calculations of the torque in your tutorial. How can you say that the torque of the joint motor is working in one direction (counterclockwise), while the motor actually creates a torque in the opposite directions for the links attached on each side?
@IHaveAQuestion, we are not sure we understand your question. The torque direction is different on each side. On the left it is counterclockwise but on the right it is clockwise. It is just that, by convention, you will have positive torque value on the left side and negative torque values on the right side.
Hi! Thank you for great tutorial.
I have a question regarding base motors. Why do we only do calculations for vertically moving motors and not for horizontally rotating one?
Hi! Thank you for step by step guide!
I have a question regarding torque. I have a 2DOF hexapod. One of servos makes leg move horizontally, another one makes it move vertically. So during torque calculation I will have both T1 and T2, right?
@Shineelove T5 and T6 give a bit of an overview of the torque needed by the “horizontal” motors; these are only really needed when walking up or down an incline. Normally if you reuse any of the motors used for vertical motion in this position, it will provide enough torque. It’s a bit of a simplification, but makes calculations and experimentation significantly easier.
@shineelove Correct. the torque required to keep the robot’s body at a height above the ground will be greater than than used to propel it in parallel to the ground. To make things easy, it’s best to simply use 12 identical motors.
Hi, thank you so much for the formula. Just a precision, what unit of calculation are you using for the actuators and links? in oz? gram? mm? cm? Thanks in advance.
@Samsara The tutorial does not make use of units - it’s equation-based. W is a measure of “weight”, L is a length, N is a force and the units of T are force times a distance. We suggest using similar units when doing your calculations (imperial vs metric etc).
Thanks once again Mr Benson for your prompt response. Just came across your forum whilst surfing the web for a better formula.
Indeed, I built a 1.8 kg homemade hexapod a couple months back using 18 dirt cheap TowerPro MG996R servos.
At that time I did a pretty straight forward diagonal torque calculation based on the MG996R which is specced circa 10kg/cm stall torque at 4.8V
My link (L2) from Coxa joint to kneel is 12 cm and the link (L1) kneel joint to foot tip is also 12 cm. The squareroot of L1+L2 is also 12 cm.
Thus, 10kg/cm specced torque of the servo * 3 legs on the ground / 12 cm gives me 2.5 kg/cm torque.
Theorically it should support a 1.8 kg robot me think. The bot could lift, walk, dance without problem, but unfortunately I have to replace a coxa servo (W2) every few days. The servo’s internal electronic circuit fried. I was wondering whether my calculation was wrong or the TowerPro is worthless. I tried to shorten the diagonal length by positioning the legs nearer to the chassis to diminish the stress of the coxa servos (W2), it seemed a little better but not the result expected.
Yep, quality has a price. The TowerPro needs a lot of soft tuning to compensate its lack of angular positioning precision. Dirt cheap but a hassle tho. I won’t go for it again if I were to build another bot. Mr Benson, do you have any recommendation for me ? Thanks in advance.