A Two-Link Inverse-Kinematic Mechanism
A Two-Link Inverse-Kinematic Mechanism
This Demonstration shows a two-linkage inverse-kinematic mechanism. The lengths of the rods shown in the diagram are and , and their angles of rotation are and , with ranges to and to , respectively. The coordinates of a point on the toroidal surface are
L
1
L
2
θ
1
θ
2
-100°
100°
-150°
150°
p
x
L
1
θ
1
L
2
θ
1
θ
2
p
y
L
1
θ
1
L
2
θ
1
θ
2
Solving for and :
θ
1
θ
2
θ
1
--++
2
L
1
2
L
2
2
p
x
2
p
y
2
L
1
L
2
1-
2
--++
2
L
1
2
L
2
2
p
x
2
p
y
2
L
1
L
2
θ
2
---
L
1
p
x
c
2
L
2
p
x
s
2
L
2
p
y
2
p
x
2
p
y
s
2
p
x
L
1
p
y
c
2
L
2
p
y
2
p
x
2
p
y
where = and =.
c
2
--++
2
L
1
2
L
2
2
p
x
2
p
y
2
L
1
L
2
s
2
1-
2
c
2
With appropriate choices of the constants, the formulas for and can be used to trace a sine wave, an ellipse, or a triangle.
θ
1
θ
2