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Karim Abdel-MalekDepartment of Mechanical Engineering and Center for Computer Aided Design (CCAD)

University of IowaIowa City, IA

(319) 335-5676amalek@engineering.uiowa.edu

1. Mathematical formulations

2. Human performance measures

3. Realistic Posture prediction

4. Object in Enclosure

5. Reach envelopes

6. Ergonomic design: Placement and layout

7. Conclusions

Overview

DIGITAL HUMAN Modeling/SIMULATION/Ergonomics

Point sp

WCS

q1

Modeling

We use kinematic methods adapted from the field of Robotics

Joint m-1

Joint m zmzm-1

Link m

Link m-1

xm-1

xm

x(q)Particularly, we use the Denavit-Hartenbergmethod for representing a kinematic chain

q1

q2

q3

q4

q5

q6

q7

q8

q9

Shoulder (5DOF), Elbow (1 DOF), and Wrist (3DOF) Model

xo

yo

X(θ)

Typically, we have used a 9DOFmodel of the upper extremitywhile accounting for the glenohumeral joint and the scapula translational motion

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sp sp

We have also modeled and analyzed the lower extremities

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Formulation

Joint Ranges

where and

Position

q1Constraint

(we consider joint ranges in the formulation by parametrizing the inequalities to equalities)

A couple of slides to demonstrate the rigor of our formulation

Jacobian

where

Three Types of Singularities

where

Formulation (continued)

(we perform Manifold Stratification to obtain all Singular behavior)

Human Performance Measures: Cost Functions

Reacheability

Workspace/Functionality

Point of interest

Fig. 13 (a) Wrist and hand (b) Modeling of the wrist joint

Dexterity

Effort

Initial Posture

Final posture

q i3( )

q f3( )

Neutral Stressed

Stress

iir

0A rii

i

Potential Energyqi

qiN

Reference

Example of a Cost Function

Potential Energy for each link of an extremityi

ir0A ri

ii

Now this can be used as a Human Performance Measure and as a Mathematical Function for Ergonomic Design!!!

Given P Posture Prediction

Joint angles

Problems with traditional Inverse Kinematics:1. Computational complexity for high numbers of degrees of freedom2. Choice of correct solution from an infinite number of solutions

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Given P and [n s a] Posture Prediction

Joint angles

Point

Posture I

Posture IIInitialPosture

Two different postures for reaching the same point.Which one is correct??

a. Inequality Constraints

b. Hand at a given location

Minimum Energy

Simple Effort

P P mii

n

i ii

ii

n

= = -

= =

Ê Ê1

0

1

( ( ))g A r

Min F w P w E = +1 2Minimization

E E w Abs q qii

n

i i iinitial

i

n

= = -

= =

Ê Ê1 1

( )

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Constraints

Solve using Genetics Algorithms

Simplified Algorithm

Target point/object perimeter

x( ) ( );11 1 1 1w w w wL U � �

x( ) ( );22 2 2 2w w w wL U � �

x( ) ( );33 3 3 3w w w wL U � �

Proposed Path

x( ) ( );44 4 4 4w w w wL U � �

x( ) ( );55 5 5 5w w w wL U � �

Y( )v

G( )u

x( ) ( );77 7 7 7w w w wL U � �

x( ) ( );76 6 6 6w w w wL U � �

Object Inside an Enclosure (Planar example)

Y( )v

x( , )u v

x( )1

x( )2

x( )3

x( )4

x( )5

x( )6

x ( )7

q2q1

s s

Ability for shoulder totranslate outside the enclosure

Reach Envelope (planar example)

This is a simple demonstrative example of planar motion of the arm modeled as a two DOF system

Point of Interest P

z0z1

z0z1

q1q2

For The curve equation is

Example (continued)

Exact Reach Envelope

x(4)

x(3)

x(1)

x

y

x(2)x(5)

p

q1

q2

q3

q4

q5

q6

q7

q8

q9

Shoulder (5DOF), Elbow (1 DOF), and Wrist (3DOF) Model

xo

yo

X(θ)

Consider the workspace of a realistic model

z0

q4

q3

For example, substitute the singular set and

4DOF Arm Example (continued)

Singular surfaces (otherwise known as barriers)These are of importancein obtaining a better understanding of the envelope

For and

q1

q3z0

4DOF Arm Example (continued)

This is the reach envelope and barriers therein in closed form.

Can be used for Design Optimization Visualization

0

1

2

3

0

0.5

1

-2

0

0

0.5

1

-2

0

Finger Workspace

x0

z0

q2

q3q4

1.51q1

z1

z2z3

1

Point P

(a) A schematic of a finger (b) Kinematic modeling of the finger as four revolute joints

Workspace of the finger

• Will be used to evaluate the degree of disability• To monitor the progress post surgery• Can be integrated to yields a number

Point of interest

Wrist’s Range of Motion (Quantifying the Workspace)

Point of interest

Example: Quantifying therange of motion after surgery

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Targetpoints

z0

x0

q1q2z1

z2

x2y2

SpecifiedPoint sp

Illustrative Example

These are points that must be touched in space

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Objective: To place a person with respect to predefined target points while minimizing or maximizing a given Cost Function

-40 -20 0 20 40-20

-10

0

10

20

30

-2-1012-20

-10

0

10

20

30

Target point sp1 (-25,-8)

Target pointsp2 (-35,12)

α

(-19.3,6.8)

Example (continued)

The workspace has automatically moved to include the target points

Initial Position and Orientation

Final Position and Orientation

Target points

Initial Position

Final position after the Placement Algorithm

Define target points Reach envelope has been identified

Cost function

Constraints (no need for inverse kinematics)

Move boundary of reach envelopeMaximize ReacheabilityMinimize ForceMaximize Dexterity (orientability)Minimize Repetitive injuries (e.g., carpal tunnel syndrome)

Satisfies Tolerance

Stop

Iterate

w = w + ∆wIterative algorithm to move the workspace

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Define human (dimension and ranges of motion)

Defined by the six generalized coordinates w that characterize its position and orientation

Example of cost functions:

Maintainability and Design• Reduce lifecycle costs by lowering maintenance requirements

• Design products to optimize maintainability

• Ensure that technicians can access parts and tools

• Anticipate strength and time requirements for maintenance tasks

Kinematics

File Anatomy Envelope Cross-Sections Placement Layout/Design Cost Functions Torques/Forces

ERGONOMICA

NewOpenCloseSaveSave AsPrintPropertiesSetup

Joints >Limbs >Torso

GenerateShowProperties >Move >RotateScaleErase

AreaVolumeMassInertia

Slice >Section >AngleDepthThickness

Shoulder >Knee >Wrist >Neck >:

Finger sizeGlove sizeFoot sizeArm size

Target points >Constraints >Forbidden Zones >

ReacheabilityDexterityCumulative TraumaStatic ForcesDynamics ForcesEnergy (Kinetic and Potential)PotentialKinetic

Measures

Define WorkspaceDefine TargetsOptimize for... >Engineering Dimensions

Define ForceDefine TorqueCalculate ForceCalculate Torque

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1. Rigorous Mathematical Methods for Ergonomics Analysis, Design, and Optimization.

2. Human Performance Measures as Cost Functions

3. Not Only Can Answer Whether a Design is Ergonomically Correct, But Can Respond With An Optimum Design

4. Ability to Augment onto JACK through a Unique Collaborative Agreement.