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Prof. Mark YimUniversity of Pennsylvania

Week 6: Inverse Kinematics

Robotics: Fundamentals

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Video 6.1Mark Yim

Robotics: Fundamentals

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Inverse Kinematics

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Where, refer to the 12 nontrivial entries of and

Inverse Kinematics Definition

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Stanford Arm Transform

12 non-linear eqns, 7 unknownsProperty of University of Pennsylvania, Mark Yim

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Approaches

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atan(y/x)

atan(y/x) vs atan2(y,x)

By Geek3 (Own work) [GFDL] By Qef (self-made using design of the bitmap version) [CC0]Property of University of Pennsylvania, Mark Yim

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Video 6.2Mark Yim

Robotics: Fundamentals

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SCARA IK

θ1

θ2d3

θ4Property of University of Pennsylvania, Mark Yim

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SCARA IK

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SCARA IK

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SCARA IK

(Px, Py)

θ1

θ2

a2a1

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(Px, Py)

θ1

θ2

a2a1

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(Px, Py)

θ1

θ2

a2a1

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(Px, Py)

αθ1

θ2

a2

a1

β

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(Px, Py)

αθ1

θ2

a2

a1

β

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SCARA IK

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SCARA IK d3

d4

d3

P

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SCARA IK

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SCARA IK

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Video 6.3Mark Yim

Robotics: Fundamentals

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Kinematic Decoupling

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Kinematic Decoupling

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Kinematic Decoupling•“gantry example.mov” Video goes here

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Kinematic Decoupling

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Inverse Position: Cylindrical robot case

pc

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q2 = d2

q1= θ1

q3 = d3x y

z

Cylindrical coordinates(RPP)

pc𝜃" = atan2 𝑦, 𝑥

𝑑, = 𝑥, + 𝑦,�

𝑑/ = 𝑧

(𝑥, 𝑦, 𝑧)

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Wrist Center Rotation

𝑇4/ =

𝑐" 0𝑠" 0

−𝑠" −𝑠"𝑑/𝑐" 𝑐"𝑑/

0 −10 0

0 𝑑"+𝑑,0 1

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q3 = d3

x y

z

1st part of SCARA(RRP)

pc (𝑥, 𝑦, 𝑧)

q1 = θ1

q2 = θ2Property of University of Pennsylvania, Mark Yim