Forward kinematics robotics m tech.

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Forward kinematics robotics m tech.

  1. 1. CS 4733, Class Notes: Forward Kinematics II1 Stanford Manipulator - First Three JointsFigure 1: Stanford Robotic Arm. The frame diagram shows the first three joints, which are in a R-R-Pconfiguration (Revolute-Revolute-Prismatic. joint θ d a α nnn1 θ1 d1 0 -90 2 θ2 d2 0 90 3 0 d3 0 0 4 5 6       C1 0 -S1 0 C2 0 S2 0 1 0 0 0  S1 0 C1 0  1  S2 0 -C2 0  2  0 1 0 0  T10 =  T2 =   T3 =    0 -1 0 d1   0 1 0 d2   0 0 1 d3  0 0 0 1 0 0 0 1 0 0 0 1     C1 C2 -S1 C1 S2 -S1 d2 C1 C2 -S1 C1 S2 C1 S2 d3 - S1 d2  S 1 C2 C1 S1 S2 C1 d 2 0  1 C2 S C1 S1 S2 S1 S 2 d3 + C 1 d 2  T20 =  T3 =    -S2 0 C2 d1   -S2 0 C2 C2 d3 + d1  0 0 0 1 0 0 0 1   1 0 0 0  0 1 0 d2  0 if θ1 = θ2 = 0, d3 = 0: T3 =   (Zero Position)  0 0 1 d1  0 0 0 1 1
  2. 2. 2 4-DOF Gantry RobotFigure 2: Gantry Robot Arm. This arm is in a R-P-R-R configuration. θ1 , θ3 , θ4 are the revolute joint angle variables andd2 is the prismatic joint variable. d4 is a constant. joint θ d a α 1 θ1 0 0 0 2 0 d2 0 -90 3 θ3 0 0 90 4 θ4 d4 0 0     C1 -S1 0 0 1 0 0 0  S1 C1 0 0  1  0 0 1 0  A0 =  A =   1  0 0 1 0  2  0 -1 0 d2  0 0 0 1 0 0 0 1     C3 0 S3 0 C4 -S4 0 0  S3  0 -C3 0  3  S4 C4 0 0  2 A3 = A =    0 1 0 0  4  0 0 1 d4  0 0 0 1 0 0 0 1 2
  3. 3.      C1 -S1 0 0 1 0 0 0 C1 0 -S1 0   S1 C1 0 0  0 0 1 0   S1 0 C1 0  A0 =  2  =   0 0 1 0   0 -1 0 d2   0 -1 0 d2  0 0 0 1  0 0 0 1 0 0 0 1       C3 0 S3 0 C4 -S4 0 0 C3 C4 -C3 S4 S3 S3 d4   S3 0 -C3 0  S4 C4 0 0   S3 C4 -S3 S4 -C3 -C3 d4  A2 =  4  =   0 1 0 0   0 0 1 d4   S4 C4 0 0  0 0 0 1  0 0 0 1 0 0 0 1     C1 0 -S1 0 C3 C 4 -C3 S4 S3 S3 d4   S1 0 C1 0  S3 C4 -S3 S4 -C3 -C3 d4   A0 = A02A24 =  4  0 -1 0 d2   S4 C4 0 0  0 0 0 1  0 0 0 1    C1 C3 C4 - S1 S4 -C1 C3 S4 - C4 S1 C1 S3 C1 S3 d4  C3 C4 S1 + C1 S4 -C3 S1 S4 + C1 C4 S1 S3 S1 S3 d4  =   -S3 C4 S3 S4 C3 C 3 d4 + d 2  0 0 0 1   1 0 0 0  0 1 0 0 if θ1 = θ3 = θ4 = 0, d2 = 0: A04=   0  (Zero Position) 0 1 d4  0 0 0 1   -1 0 0 0  0 0 1 d4 if θ1 = θ3 = θ4 = 90, d2 = D: A 4=  0   0 1 0 D  0 0 0 1 3

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