the robotic arm tutorial

[Marwan]

Hi,

After I read the robot arm tutorial, I asked myself: “what could prevent the vertical arm from leaning?” (the attached picture can clarify my point). I looked at the robot arm calculator but I didn't find anything mentioned about that. I did some math and I want to review it with you:

TL = (W0 * Sin (theta) * L0/2) + (W1 * Sin (theta) * L0) + (W2 * Sin (theta) * L0) + (W3 * Sin (theta) * L0) + (W1 * Cos (theta) * L1/2) + (W2 * Cos (theta) *(L1 + L2/2)) + (W3 * Cos (theta) * (L1+L2+L3/2))

= (W0/2 + W1 + W2 + W3) * L0 * Sin (theta) + (W1 * Cos (theta) * L1/2) + (W2 * Cos (theta) *(L1 + L2/2)) + (W3 * Cos (theta) * (L1+L2))

I neglected the weight of motors in order not to make the equation complicated, but I’m going to consider them later in my equation

TL: Torque around the fixed point.
W0, W1, W2, W3: The weights of the vertical, first, second linkage and load.
L0, L1, L2: The lengths of vertical, first and second linkage
Theta: leaning angle.

Do I miss something?
Now I want to get the optimum lengths of linkages that do not make the arm lean, if I’m given the weights and theta is 1 or 2 degrees, how can I continue?



If you can't see the image, please follow the link:
http://img301.imageshack.us/my.php?image=armleanyn5.jpg

[Admin]

When you say leaning, about which joint/link do you mean?

The minimum required calculated torque about that joint is the torque needed to prevent it from 'leaning'. Also, you don't need any trig here - everything should be perfect 90 degree angles if there is no 'leaning'

Also, the equations basically determine an effective moment (torque), so you wouldn't need to do any trig until after you have your 90 degree angle solution done.

[Marwan]

When you say leaning, about which joint/link do you mean?

Please make a look on the image to get what I mean



alright, I'm gonna make theta = 0 "from the drawing that means no leaning". I may choose the suitable motors with suitable torques but the group may be too heavy to be carried by the vertical arm.

[Admin]

Hmmmm your image is a dead link

[izua]

imageshack kicks (its own) ass.

[Admin]

One way to counter that leaning torque is to put a heavy counter-weight on the other end of the arm, as I did on this bot:
http://www.societyofrobots.com/robot_arm_card_dealer.shtml

(notice the yellow batteries)

[Marwan]

Thank you guys