3 Robotic Systems Kinematics

7/29/2019 3 Robotic Systems Kinematics

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Robotic Systems(3)

Dr Richard Crowder

School of Electronics and Computer Science


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Robot Kinematics

Requires a unified approach to identify the variables of arobots or manipulator's joints and links.

Robotics depends on the use of right handed Cartesian

frames of reference.

X

Y

Z

+ve rotation


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Link - 1

A link holds two joints apart.

The axes of the joints are always along the Z axis of theoriginating frame.

The link axis is always along the X axis of the originatingframe.

The normal displacementbetween the two frames is giventhe symbol, a.

The twist angle between the two joint frames is given thesymbol, .


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Link - 2

a

Joint 1

Joint 2

Note direction of

rotation


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Link - 3

Z1

Z2

X1

Y2

J1

J2

X2

Y2

a1

Joint displacement = a1

Twist angle = 1 = 270o or -90o

1


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Joint

Rotary or Prismatic identical kinematic geometry

The displacement between two links is along the Z-axis and is given

the symbol d, and is the variable in the prismatic joint.

The angle between the two links is , and is the variable in a revolutejoint.

Link 1

Link 2

Z1

Z2

X1

Y1

X2d1

1


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Geometric parameters

A manipulator consists of a collection of joints and links,organised intojoint-link pairs.

While the sequence through the manipulator chain is

arbitrary, the selection should minimised the number of variables,

and reflect the mechanical arrangement,

and the sense of rotation of a revolute joint.

The effect of reversing the sense changes a variable from to 360- .


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Example

Joint 5

S1

S2 S3

S4

Joint 1

Joint 4

Joint 2

Joint 3

Determine the 5 joint-link

Pairs for the manipulator


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Joint 1

1d

q

a

a

S1

S2 S3

S4

Joint 1

Joint 4Joint 2

Joint 3


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Joint 2 and Joint 3

2 3

d

q

a

a

S1

S2 S3

S4

Joint 1

Joint 4Joint 2

Joint 3


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Joint 4

Joint 4

Joint 5

4d

q

a

a

S1

S2 S3

S4

Joint 1

Joint 4Joint 2

Joint 3


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Joint 5

5d

q

a

a

S1

S2 S3

S4

Joint 1

Joint 4Joint 2

Joint 3


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Example

S1

S2 S3

S4

Joint 1

Joint 4

Joint 2 Joint 5

Joint 3

i 1 2 3 4 5

di S1 0 0 0 S4

qi 1 2 3 4 5

ai 0 S2 S3 0 0

ai 270 0 0 90 0


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Example 2

S1

Joint 3 S3

S4

Joint 1

Joint 5

Joint 2 Joint 6

Joint 4 Determine the 6 joint-link


i 1 2 3 4 5 6

di S1 0 S2 0 0 S4

qi 1 2 0 4 5 5

ai 0 0 0 S3 0 0

ai 90 90 270 0 90 0


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Example 3

Joint 2

Joint 4

S4

Joint 1

Joint 3

Joint 6

Joint 5

Determine the 6 joint-link



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Example 4

Joint 1

Joint 2

Joint 3

Tool

Interface

3 Robotic Systems Kinematics

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