Society of Robots - Robot Forum
Mechanics and Construction => Mechanics and Construction => Topic started by: Marwan on April 24, 2008, 02:48:31 AM
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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?
(http://img301.imageshack.us/img301/9403/armleanyn5.th.jpg)
If you can't see the image, please follow the link:
http://img301.imageshack.us/my.php?image=armleanyn5.jpg (http://img301.imageshack.us/my.php?image=armleanyn5.jpg)
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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' ;D
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.
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When you say leaning, about which joint/link do you mean?
Please make a look on the image to get what I mean
(http://img301.imageshack.us/img301/9403/armleanyn5.th.jpg)
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.
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Hmmmm your image is a dead link :P
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imageshack kicks (its own) ass.
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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)
(http://www.societyofrobots.com/images/robot_arm_dealer_table.JPG)
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Thank you guys :-*