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Find inverse kinematics for Four ax is SCARA robot.
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Solution:

Four-axis robot:

Following is the kink-coordinate diagram for a four-axis articulated robot:

enter image description here

To solve the inverse kinematics, we use the tool configuration vector as follows:

W(q)=[a1C1+a2C12a1 S1+a2 S12 d1q3d400exp(q4/π)]

w21+w22=a21+2a1a2C2+a22

q2=±arccosw21+w22a21a222a1a2

(a1+a2C2)C1+(a2S2)S1=w1(a2S2)C1+(a1+a2C2)S1=w2

S1=a2S2w1+(a1+a2C2)w2(a2S2)2+(a1+a2C2)2C1=(a1+a2C2)w1a2S2w2(a2S2)2+(a1+a2C2)2

q1=atan2[a2S2w1+(a1+a2C2)w2,(a1+a2C2)w1a2 S2w2]

q3=d1=d4w3

q4=πln|w6|

q4=q1q2q124

Complete Solution:

Following is the complete algorithm for a four-axis SCARA robot.

enter image description here

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