CS

CE

452

In

tro

to

Ro

bo

tics

Question Set 3 – Inverse Kinematics

1

CS

CE

452

In

tro

to

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bo

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C

SC

E 4

52 I

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o t

o R

ob

oti

cs

PPR

z0

y0

0(z3, y3) α3

Given 0(z3, y3, α3) and frame {0}, perform the following tasks:

• Attach frames {1}, {2}, and {3} to the robot

• Draw (d1, d2, 3) on the figure

• Find (d1, d2, 3) as the function of 0(z3, y3, α3)

x0

L2

CS

CE

452

In

tro

to

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C

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E 4

52 I

ntr

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ob

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cs

PPR

Z0,1

y0

0(z3, y3)

α3

Given 0(z3, y3, α3) and frame {0}, perform the following tasks:

• Attach frames {1}, {2}, and {3} to the robot

• Draw (d1, d2, 3) on the figure

• Find (d1, d2, 3) as the function of 0(z3, y3, α3)

x1

Z2

Z3

x0

x2

x3

d2

d1

L2 3

CS

CE

452

In

tro

to

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bo

tics

C

SC

E 4

52 I

ntr

o t

o R

ob

oti

cs

PPR

Z0,1

y0

0(z3, y3)

α3

Given 0(z3, y3, α3) and frame {0}, perform the following tasks:

• Attach frames {1}, {2}, and {3} to the robot

• Draw (d1, d2, 3) on the figure

• Find (d1, d2, 3) as the function of 0(z3, y3, α3)

x1

Z2

Z3

x0

x2

x3

d2

d1

L2 3

CS

CE

452

In

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to

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E 4

52 I

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cs

RPR Robot

x0

y0

0(x3, y3) α3

1

3γ

Given 0(x3, y3, α3) and frame {0}, perform the following tasks:

• Attach frames {1}, {2}, {3} to the robot

• Draw (1, d2, 3) on the figure

• Find (1, d2, 3) as the function of 0(x3, y3, α3)

L2

CS

CE

452

In

tro

to

Ro

bo

tics

C

SC

E 4

52 I

ntr

o t

o R

ob

oti

cs

RPR

x0

y0

0(x3, y3) α3

90+1

3γ

d2

L2

φZ0,1

Z2

Z3

Given 0(x3, y3, α3) and frame {0}, perform the following tasks:

• Attach frames {1}, {2}, and {3} to the robot

• Draw (1, d2, 3) on the figure

• Find (1, d2, 3) as the function of 0(x3, y3, α3)

x1

-1

x2

x3

CS

CE

452

In

tro

to

Ro

bo

tics

C

SC

E 4

52 I

ntr

o t

o R

ob

oti

cs

RPR

x0

y0

0(x3, y3) α3

90+1

3γ

d2

L2

φZ0,1

Z2

Z3

Given 0(x3, y3, α3) and frame {0}, perform the following tasks:

• Attach frames {1}, {2}, and {3} to the robot

• Draw (1, d2, 3) on the figure

• Find (1, d2, 3) as the function of 0(x3, y3, α3)

x1

-1

x2

x3

22

23

232 Lyxd

90)/arctan(),(2tana

)/arctan(),(2tana

)/arctan(90

22331

2233

221

dLxy

dLxy

dL

133

33