Differential

Motions and

Velocities

EENG428 INTRODUCTION

TO ROBOTICS

Differential Motions and Velocities • Differential Motions

• Small movement of robot mechanisms

• Small period of time

• Differential Relationships

Differential Motions and Velocities

Jacobian

• Representation of the geometry of the elements

of a robot mechanism in time

• Relationship between the individual joint motions

and overall mechanism motions

Jacobian

Jacobian

Differential Motions of a Frame

• Differential motions of a frame:

• Differential Translations

• Differential Rotations

• Differential Transformations (Translations &

Rotations)

Differential Motions of a Frame

• Differential Translations

(dx, dy, dz)

• Differential Rotations

(δx, δy, δz)

Use approximations → sin δx= δx, cosδx= 1

Neglect higher order terms → ,

etc…

2( x) x

Differential Motions of a Frame

Differential Motions of a Frame

Differential Motions of a Frame

Differential Motions of a Frame

Differential Motions of a Frame

Differential Motions of a Frame

radians

Differential Motions of a Frame

Interpretation of the Differential Change

Interpretation of the Differential Change

Differential Changes between Frames

Differential Changes between Frames

Differential Changes between Frames

Differential Changes between Frames