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Haptic Systems 530-655

Mohsen Mahvash Lecture 29/1/06

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Tip of a kinesthetic Haptic display and degrees of freedom

Relation between the tip position and joint angles

Encoders and measuring joint angles

Relation between joint torques and forces at the tip

Jacobean

Actuator equations

Nonidealities of a haptic device

Discussion

References

Generating Force-Feedback with a Manipulator

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A point of haptic display whose position and orientation are used for haptic simulation

Through this point human user interacts with haptic systems

Haptic simulator defines the force and torques should be generated

at this point by the manipulator

Degrees of freedom of a haptic display:

The number of directions that a haptic display can pivot or move its tip

DOF of motion

DOF of sensing

DOF of actuation

Tip of a Kinesthetic haptic display

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Tip Location and Degrees of Freedom

Tip

SensAble Phantom Omni

DOF of motion: 6

DOF of sensing: 6

DOF of actuation: 3

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Tip Location and Degrees of Freedom

Tip

MPB 6S

DOF of motion: 7

DOF of sensing: 7

DOF of actuation: 6

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Tip Location and Degrees of Freedom

Tip

da Vinci Master (From US Patent 06714839)

DOF of motion: 7

DOF of sensing: 7

DOF of actuation: 7

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Tip Location and Degrees of Freedom

Tip?

Haptic scissors

DOF of motion: 2

DOF of sensing: 2

DOF of actuation: 2

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Relation Between Tip Position and Joint Angles(Forward Kinematics)

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)sin()cos()sin( 333221 lllr

1l

2l 3l

2

1)cos( 1rpx

)sin( 1rpy

)cos()sin()cos( 333221 lllpz

P

0y

0z

0x

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Encoders

Small discs that have holes in them that can be read by photo sensors. The photo sensors record the number of transitions between light and dark.

Photo detector

Light beam generator

Disc

Initializations:Potentiometers and fixed setting points

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Relation between Joint Torques and Forces at the tip

Principal of virtual work

Jacobian

.. XF

TT JF

JX

TT JF

FJ T

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Jacobian

)sin()cos()sin( 333221 lllr

)cos( 1rpx

)sin( 1rpy

)cos()sin()cos( 333221 lllpz

yxx frfr )cos()sin( 11

zyxy flflfl )sin()2cos()sin()2cos()cos( 211111

z

yxz

fll

fllfll

))sin()cos((

)sin(*))cos()sin(()cos(*))cos()sin((

3332

1333213332

111 / xpJ

121 / ypJ

121 / ypJ

JX

Taking partial derivatives

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Actuators Equations

Torque

Voltage

Input

Ikt

KE

ERIdt

dILV

Current amplifier: I as an input

Voltage amplifier: V as an input

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Nonidealities of a haptic device

Ideal haptic devices No friction No Inertia High bandwidth

KIFhand

Actual haptic devices

handfriction FFIHGXCXM )(

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Discussion

High fidelity haptic devices Friction Inertia gravity Device bandwidth Sensors Actuators

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Tomorrow

Introduction to haptic rendering

References

Introduction to Robotics Mechanics and Control, 2nd Ed., John J. Craig, Addison- Wesley (Chapter 3 and 5.7 to 5.11)