Passive Dynamic Bipedal Walking with Knees

The Effect of Parameter Variation

Derek Koop, Dean Ferley and Christine Qiong Wu

Department of Mechanical and Manufacturing Engineering

University of Manitoba

2008 North Central ASABE/CSBE Conference

What is passive dynamic walking ?� Passive walking:

A natural steady gait maintained by gravitational forces.-no actuators

� Static vs Dynamic Walking:� Static vs Dynamic Walking:

A static walking mechanism maintains static equilibrium throughout its motion while a dynamic walking mechanism does not.T. McGeer. (1990). “Passive Dynamic Walking,” [Online], pp. 62-82. Available: Sage Journals Online http://ijr.sagepub.com.proxy1.lib.umanitoba.ca/cgi/reprint/9/2/62 [Sept 17, 2008].

What purpose does it serve ?

� Understanding the natural dynamics behind bipedal locomotion.

� Reduces energy requirements when incorporated into actuated designs

T. McGeer. (1990). “Passive Dynamic Walking,” [Online], pp. 62-82. Available: Sage Journals Online http://ijr.sagepub.com.proxy1.lib.umanitoba.ca/cgi/reprint/9/2/62 [Sept 17, 2008].

Our walker – Dexter Mk II

Dexter Mk II - Terminology

Thigh

- Leg Angle

- Step Angle

- Step Length

Shank

- Step Length

Data Collection

Parameters Varied

� Ramp Angle� Home configuration

24

28

32

36

Ste

p L

ength

(cm

)� Foot Design

20

3.75 4.25 4.75 5.25 5.75 6.25

Ramp Angle (degrees)

F1 F2 F3

Parameters Varied� Limb length

� Thigh and shank are proportional

� Thigh and shank are mismatched

� Mass Ratio� Mass Ratio

� Mass addedA. Greaves and I. Lohrenz, A Study in Passive

Dynamic Walking, B. Sc. thesis, Department of

Mechanical Engineering, University of

Manitoba, Winnipeg, Manitoba, 2008.

Dynamic Parameters

� Key Dynamic Parameters that affect the gait pattern:� Radius of Gyration

� Center of Mass

Radius of Gyration = Mass Moment of Inertia� Radius of Gyration = Mass Moment of InertiaMass

� Center of Mass is measured from the hip downward

25

26

27

28

29

Ste

p A

ng

le (

deg

rees

)

Thigh-Shank Mismatch

Mass Distribution

Proportional Thigh-Shank

27

28

29

Ste

p A

ng

le (

deg

rees

)

Thigh-Shank Mismatch

Mass Distribution

Proportional Thigh-Shank25

26

27

28

29

Ste

p A

ng

le (

deg

rees

)

Thigh-Shank Mismatch

Mass Distribution

Proportional Thigh-Shank

Study Comparison

24

32 34 36 38 40 42

3.3

3.4

3.5

3.6

46 48 50 52

Dim

ensi

on

less

Ste

p P

erio

d

Radius of Gyration / Leg Length (%)

3.3

3.4

3.5

3.6

32 34 36 38 40 42

Dim

ensi

on

less

Ste

p P

erio

d

Center of Mass / Leg Length (%)

24

25

26

46 47 48 49 50 51 52

Ste

p A

ng

le (

deg

rees

)

Radius of Gyration / Leg Length (%)

24

46 48 50 52

Proportional Thigh-Shank Study� Originally seems anomalous

� Individual link properties analyzed

55

60

Rad

ius

of

Gyra

tio

n (

%)

50

Cen

ter

of

Mas

s (%

)

40

45

50

55

1 2 3 4 5 6

Rad

ius

of

Gyra

tio

n (

%)

Trial

2.3 3.1 3.2 3.3 3.4 3.5

20

30

40

1 2 3 4 5 6

Cen

ter

of

Mas

s (%

)

Trial

2.3 3.1 3.2 3.3 3.4 3.5

Double Pendulum Simplification

Summary� That the radius of gyration and center of mass are the key dynamic parameters that effect the gait pattern.

� For non-uniform walkers use a double For non-uniform walkers use a double pendulum simplification.

Questions ?