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  • 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

  • 1

    21

    2

    1

    2

    1

    2

    Capstan drive

    Friction drive

    transmission

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

  • pulley

    sector rpulley

    rpulleypulley = rsectorsector

    xhandle = rhandlesector

    xhandle =rhandlerpulley

    rsectorpulley

    rsector

    rhandle

    xhandle

    Hapkit kinematics

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

  • position, velocity, and acceleration

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

    position

    time0

    velocity

    time0

    t

    acceleration is usually too noisyvavg =

    x

    t

    vinst =dx

    dt= x

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

  • rpulley

    rsector

    rhandle

    Fhandle

    pulley

    sector

    pulleyrpulley

    =sectorrsector

    Fhandle =sectorrhandle

    Fhandle =rsector

    rhandlerpulleypulley

    = Frrelationship betweenforce and torque:

    Hapkit force/torque relationships

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

  • forward kinematics for higher degrees of freedom

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

    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

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

  • formulating the Jacobian

    multidimensional form of the chain rule:

    x =@x

    @q1q1 +

    @x

    @q2q2 +

    y =@y

    @q1q1 +

    @y

    @q2q2 +

    ...

    xy

    =

    "@x@q1

    @x@q2

    @y@q1

    @y@q2

    # q1q2

    x = J q

    assemble in matrix form:

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

  • 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

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

  • 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

    fTJq = T q

    fTJ = T

    JT f =

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

  • simplified dynamics

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

  • mass-damper model

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

  • free body diagram

    Fb = bx,

    sum forces, equate to inertia:

    mx = Fa Fb

    mx + bx = FaStanford University ME 327: Design and Control of Haptic Systems Allison M. Okamura, 2018

  • system block diagram

    Computer

    xd hk

    dtd hb

    hk

    hb

    h

    m1 dt dt

    fb

    ( ) 12 TJ ? cmd TJ1 tEnvironmenVirtual

    -

    -

    +-

    +-

    fhand

    ftotal xh xh xh +- fa +

    -

    fcmd

    xd

    -

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

    human

    device

  • rendering a wall (in one degree of freedom)

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

  • 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

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

  • 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

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

  • rendering a simple wall

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

  • when the tool is not a point

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

  • 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

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

  • 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:

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

  • displaying impact vibrations

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

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

  • aside: wall realism evaluation

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

    Kuchenbecker, et al. 2006

  • kinesthetic device examples

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

  • K. KuchenbeckerStanford University ME 327: Design and Control of Haptic Systems Allison M. Okamura, 2018

  • K. KuchenbeckerStanford University ME 327: Design and Control of Haptic Systems Allison M. Okamura, 2018

  • K. KuchenbeckerStanford University ME 327: Design and Control of Haptic Systems Allison M. Okamura, 2018

  • Types of Devices

    Florian Gosselin, CEAStanford University ME 327: Design and Control of Haptic Systems Allison M. Okamura, 2018

  • Types of devices

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

  • 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

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

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

    (return in class today if not done already)

    Stanford University ME 327: Design and Control of Haptic Systems