Lecture 2: Kinesthetic haptic devices - Stanford...

ME 327: Design and Control of Haptic Systems Winter 2018

Lecture 2:Kinesthetic haptic devices:

design, kinematics and dynamics

Allison M. OkamuraStanford University

kinematics

Stanford University ME 327: Design and Control of Haptic Systems © Allison M. Okamura, 2018

✓2✓1

Capstan drive

Friction drive

transmission

✓pulley

✓sector rpulley

rpulley✓pulley = rsector✓sector

xhandle = rhandle✓sector

xhandle =rhandlerpulley

rsector✓pulley

rsector

rhandle

xhandle

Hapkit kinematics

position, velocity, and acceleration

In this class, you will measure position and time data directly from your Hapkit

position

velocity

acceleration is usually too noisyvavg =

vinst =dx

rpulley

rsector

rhandle

Fhandle

⌧pulley

⌧sector

⌧pulleyrpulley

=⌧sectorrsector

Fhandle =⌧sectorrhandle

Fhandle =rsector

rhandlerpulley⌧pulley

⌧ = Frrelationship betweenforce and torque:

Hapkit force/torque relationships

forward kinematics for higher degrees of freedom

for mechanical trackers that use joint angle sensors, you need a map between joint space and Cartesian space

fwd kinematics: from joint angles, calculate endpoint position

computing end-effector velocity

• forward kinematics tells us the endpoint position based on joint positions

• how do we calculate endpoint velocity from joint velocities?

• use a matrix called the Jacobian

x = J q

formulating the Jacobian

multidimensional form of the chain rule:

@q1q1 +

@q2q2 + · · ·

@q1q1 +

@q2q2 + · · ·

"@x@q1

# q1q2

x = J q

assemble in matrix form:

compute the necessary joint torques

the Jacobian can also be used to relate joint torques to end-effector forces:

this is a key equation for multi-degree-of-freedom haptic devices

⌧ = JT f

how do you get this equation?

the Principle of virtual workstates that changing the coordinate frame does not change the total work of a system

f · �x = ⌧ · �qfT �x = ⌧T �q

fTJ�q = ⌧T �q

fTJ = ⌧T

JT f = ⌧

simplified dynamics

mass-damper model

free body diagram

Fb = bx,

sum forces, equate to inertia:

mx = Fa – Fb

mx + bx = Fa

system block diagram

Computer

dtd hb

m1 ∫ dt ∫ dt

( ) 12−TJ ? cmdτ TJ1 tEnvironmen

Virtual

ftotal xh xh xh +- fa +

device

rendering a wall (in one degree of freedom)

1. read the position of the user from the haptic display

2. see if there is a collision with objects in the virtual environment

3. if there is, calculate forces

4. send corresponding torque commands to motors, and change the virtual environment state

classic algorithm for renderingwith an impedance-type device

• the virtual environment pretends that the user is holding onto a fictional rigid body though the haptic device handle

• this rigid body interacts with other “rigid” bodies in the virtual environment.

• with impedance control, nothing is perfectly rigid: F = kx

static rigid body interaction

rendering a simple wall

when the tool is not a point

in what ways does this algorithm feel like a real wall?

in what ways does it not?

how could you make it feel more like a real wall?

discussion

visual feedback of stiffness

• trick: never show the point penetrating the surface, even if it is

• psychophysical studies have shown that this makes the surface appear stiffer/harder

Actual:

Visual display:

displaying impact vibrations

Kuchenbecker, et al. 2006Okamura, et al. 2001

aside: wall realism evaluation

Kuchenbecker, et al. 2006

kinesthetic device examples

Types of Devices

Types of devices

kinesthetic device challenges• competing goals of high stiffness and low mass

• force feedback feels soft - “Nerf World”

• point-based interactions are overly simple

• devices of sufficient quality are expensive

• limited workspace size, degrees of freedom, and actuation power

• usually constrained to sit at a desk

• no programmable tactile feedback

fill out the survey http://www.stanford.edu/class/me327/assignments/survey.pdf

(return in class today if not done already)

pay lab materials fee ($50 check made out to Stanford University, by class time Thursday 9/18)

do Assignment #1 http://web.stanford.edu/class/me327/#c3do your 3D printing as early as possible!

attend seminar tomorrow 12-1 pm, with Mark Cutkosky in 420-040 (Jordan Hall)

Assignment 1 due 1/18

1. Readings (no pts.)

2. Design and 3D print your Hapkit handle (10 pts.) Can start tomorrow 1/12

3. Haptics application ideas (10 pts.)

4. Haptic device simulation (30 pts.) We will notify you when the electronic submission folders on Box are ready

Office Hours• Jake: Mondays 10-11 am in 520-145

• Nathan: Wednesdays 3-5 pm in 520-145

• Allison: TBD

• 520-145 (D'Arbeloff Teaching Lab) schedule is online

• You can also post questions to piazza

• You can also email us for an appointment (please email all three of us and be sure to state your available times for the next couple of days)

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