'Bio-inspired Mechanism Design'라는 주제로 Adapting and Overcoming Unstructured Environments (생체모방로봇)에 대한 메커니즘 기술을 발표함.

1. 서울과학기술대학교 기계자동차공학과
생체모사디자인 실험실
정광필
Bio-inspired Mechanism Design
for Adapting and Overcoming Unstructured Environments

2. Brief History of Mechanism Design
DaVinci, 15th century~
Rigid Linkage Mechanisms

3. Brief History of Mechanism Design
Paros & Weisbord, 1965~ C. Laschi, 2007~
Compliant Mechanisms Soft Mechanisms

4. Brief History of Mechanism Design
Rigid Linkage
Mechanisms
DaVinci, 1450s~
Paros & Weisbord, 1965~
Compliant
Mechanisms
C. Laschi, 2007
Soft Mechanisms
Precise path generation Highly Adaptive
Harvard, 2011

5. Brief History of Mechanism Design
Human muscle Lift heavy rocks
DaVinci, 1450s~
Actuator Transmission Desired motion

6. Brief History of Mechanism Design
Motors/Engines Precision control
Actuator Transmission Desired motion
C. W. Musser, 1957~Planetary gears

7. Brief History of Mechanism Design
C. Laschi, 2007~
Soft Mechanisms
Adaptive motion
Actuator Transmission Desired motion
Pneumatic/
Tendon/
Smart actuators

8. Brief History of Mechanism Design
Human muscle Lift heavy rocks
Motor/Engine Precision control
Actuator Desired motion
Adaptive motion
Transmission
Pneumatic/
Tendon/
Smart actuators

9. Soft Mechanisms
Soft, flexible, stretchable
C. Laschi, 2007~

10. Bio-inspired Mechanisms
Case Western Univ.UC Berkeley
Bio-Inspired Design Biomimetic Design

11. Bio-inspired Mechanisms
L. H. TING, et al, J Exp Biol, 1994
UC Berkeley, 2016
Alternating Tripod Gait Highly Compliant
1. Extract key principles
2. Use best engineering solutions
3. Embed control to body parts : tuned leg, feet, etc.
R. Full, UC Berkeley

12. Flexural Buckling based
Underactuated Adaptive Gripping
Mechanism
The Buckling gripper –
dimensions of 15mm×10mm×6mm
and weight of 140 mg
The Buckling Hands
IEEE Transactions on Robotics, 2013

14. Biological Inspiration
Hydroskeleton body Planta
R. E. Snodgrass, Principles of insect morphology, 1935
Retractor Muscles Multiple Segments
http://www.performance-vision.com/cecropia/cecropia5.htm
www.padil.gov.au/maf-order/Pest/Main/141501/35906

15. Concept Design
Front view of a single segment Front view of multiple segments

16. Operation
Release the bar.
Locate the gripper to the target.
SMA actuator pulls the bar to open the spines.

17. Flexural Buckling enables Adaptive Gripping
Behavior of Flexural Buckling

18. Pseudo-rigid-body Model
The bio-inspired gripper Equivalent model
H.J. Su, J. of Mechanisms and Robotics, 2009
1 1 1
1 2 3
1 2 3' ' '
( ) 0af k k k
d d d
  
  
  
  
   
  
1 2 3
1 2 3
1 2 3 '
1
( ) 0s sf l k k k
l
  
  
   
  
  
    
  
'
1 1 0 2 01 3 012 4 3 0123( ) ( / 2) 0l C C C l l C         
' '
1 1 0 2 01 3 012 4 3 0123( ) ( / 2)l S S S l l S d         
0 1 2 3         
Larry L. Howell, Compliant mechanisms, 2001

19. Contact Force Measurement
Force level
Gripping range
Flexure length
Force variation
maxGR 
max
0
max
1
( )L cF f d

 

 
max 2
0
max
1
( ( ))V L cF F f d

 

 

20. Simulations on Contact Forces
Short
Long

21. Gripping Natural Surfaces

22. Scalable Buckling Hand

23. Compliant Leg Analysis of
Flea-inspired Jumping Mechanism
IROS, 2014
Bioinspiration&Biomimetics, 2016

24. What is different from other jumps?
Run-upPeriodic Burst
Higher speed with
improved energy
efficiency without
endangering stability.
Input kinetic energy is
different depending on
run-up skills.
Input energy is fixed.

25. Conversion Efficiency of Jumping Robots
Representative Efficiency for Jumping Robots
W: energy input (Generally kinetic energy)
d: moved distance
P: power input at velocity, v
R. M. Alexander, Principles of Animal
Locomotion, 2003
Kinetic energy
Initially Stored
Energy
output (mg x d)
Conversion Efficiency Cost of transport
COT does not count losses
during conversion of stored energy to kinetic energy.
𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑑 𝐸𝑛𝑒𝑟𝑔𝑦
𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑙𝑦 𝑆𝑡𝑜𝑟𝑒𝑑 𝐸𝑛𝑒𝑟𝑔𝑦
Conversion Efficiency:
J. Burdick, Int. J. Robot.
Res., 2003
𝑊
𝑚𝑔𝑑
Cost of transport:

26. Compliant Leg in Jumping Insects
Burrows et al., J. Exp.
Biol., 2002
Considerable bending of the
hind-leg tibiae occurred during
the acceleration phase of the
jump.

27. Similarly, the mechanism takes off with its leg
being bent.
This may seem inefficient since the energy
is consumed as leg vibration.
Instant of take-off: Vertical reaction force = 0
Leg bending stiffness
0.0102 Nm/rad
Problem define
Bent Leg at the Moment of Take-off

28. A Milli-Scale Jumping Mechanism
Leg bending stiffness
0.0102 Nm/rad
0.0469 Nm/rad 0.0869 Nm/rad
Problem define
5000fps
- Jumping behavior differs depending on the leg stiffness.
- Take-off finishes with 30ms.
- Acceleration increases up to 500m/s2.

29. Storage Trigger Release
Four-bar linkage transmits the store energy!
Design concepts
Triggering
actuator
Linear
spring
Four-bar Linkage as Transmission

30. Analysis
Compliant Leg Modeling
0.0469 Nm/rad
Option 1. Commercial Dynamic FEM
simulator
- Precise
- Takes long time to calculate
- Difficult to change parameters
Option 2. Simplified model
- A bit inaccurate
- Fast calculation
- Easy to change parameters

31. Analysis
Compliant Leg Modeling
Larry L. Howell, Compliant Mechanisms, 2001
- Five bodies
- 3 DoF

32. Dynamics
- Kinematics

33. Four-bar Linkage Dynamics
- Energy and Lagrangian
- Reaction force - Take-off velocity
- Kinematic coefficient
- Four-bar linkage relation

34. 0.0869Nm/rad 0.6746Nm/rad Rigid case
Analysis
Simulated Results

35. Sample No. Bending stiffness (Nm/rad) Material Thickness (mm)
1 0.0078 GFRP 0.58
2 0.0248 GFRP 0.64 (6mm width)
3 0.0434 GFRP 0.64 (4mm width)
4 0.1288 GFRP 0.39
5 0.3373 CFRP 0.27
Design concepts
Experiment

36. 0.0102Nm/rad 0.0869Nm/rad 0.6746Nm/rad
Analysis Experiments
Comparison with Experiments and Simulation

37. 0.0102Nm/rad
In the compliant case,
- Takes less time to take-off
- The compliant leg does not support the thrusting force.
Take-off time
Take-off time
Experiments
0.0869Nm/rad
Result 1. Compliant Leg Reduces Take-off Time

38. Result 2. There Exists an Optimal Compliance

39. Froghopper-inspired
Steerable Jumping Robot
Bioinspiration&Biomimetics, 2016

40. 1.1 g flea-inspired jumping mechanism
Latch Storage Trigger Release
Torque reversal by Trigger muscle !
Noh et al., 2012
How to Steer?

41. Steerable Jumping Robots
Steering mechanisms
Zhao et al., Trans.
Robot., 2013
Kovac et al., Auton
Robot, 2010
Steering after landing Rotating the external cage
Armour et al., Bio. Bio.,
2007
Changing center of mass
Kovac et al., Auton Robot, 2010

42. Steering Mechanisms of Locust
Elevation Control in Locust
G. P. Sutton et al, J. Comp. Physiol. A, 2008
- Dual energy storage
- Reaction force passes through COM
- Changing the initial positions of hind legs

43. Steering Mechanism of Froghopper
FxFx
Fy Fy
Fx
Fy
Fx
Fy
Fx Fx
FyFy
G. P. Sutton et al, J. Exp. Bio.,
2010
Frog hopper’s Moment Canceling
- Dual energy storage
- Moment canceling & Synchronization
- Jumps without much rotation
Sutton et al., J. Exp.
Biol., 2010

44. Mechanism Design – Jump & Synchronization
- Dual energy storage
=> 1 storage/leg
Storage Release Synchronization
- Timing synchronization
=> Gear

45. Mechanism Design
Storage Synchronization & Release

46. Mechanism Design – Jump & Synchronization
Direction change (400fps)

47. Direction of Reaction Force

48. Direction of Reaction Force = Angle of Tibia
Jump Direction = Average Angle of Both Tibiae.

49. Jumping direction corresponds to the average angle of both tibiae.
0ms 7.14ms 14.28ms-7.14ms-14.28ms-21.43ms
0ms 7.14ms 14.28ms-7.14ms-14.28ms-21.43ms
Jump Direction = Average of Tibia Angle

50. Jumping direction corresponds to the average angle of both tibiae.
0ms 7.14ms 14.28ms-7.14ms-14.28ms-21.43ms
0ms 7.14ms 14.28ms-7.14ms-14.28ms-21.43ms
Jump Direction = Average of Tibia Angle

51. Asynchronous & Single-legged Jump
Single-legged jumpAsynchronous jump
420 FPS420 FPS

52. Jump Direction = Average of Tibia Anlge
Asynchronous operation
dose not affect jump direction!

53. Kinetic Energy Analysis

54. Jumping Leg Design
- Symmetrically arranged legs
- Synchronous operation
=> Moment cancel out
=> Reduced body rotation
Femur
(mm)
Coupler
(mm)
Robot 1 10 16
Robot 2 16 16
femur
tibia
coupler

55. Predicting Jump Direction
Tibia Femur
𝐿 𝑡𝑖𝑏𝑖𝑎 𝐹𝐺 𝑥
cos 𝜃 𝐿 − 𝐿 𝑡𝑖𝑏𝑖𝑎 𝐹𝐺 𝑦
sin 𝜃 𝐿 ≈ 0
∴ 𝑡𝑎𝑛 𝜃 𝐿 =
𝐹 𝐺 𝑥
𝐹 𝐺 𝑦
- Due to freely rotating knee joint, net torque on tibia is almost zero:
Direction of reaction force from ground = Angle of tibia
=> Jump direction can be controlled by tibia posture.
∴ 𝜃𝐽𝑢𝑚𝑝 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛≈
𝜃𝑡𝑖𝑏𝑖𝑎,𝐿 + 𝜃𝑡𝑖𝑏𝑖𝑎,𝑅
2
Knee-joint
Tibia
Femur
θL
(-)
θR
(+)

56. Steerable Jumping Robot
1000fps
Rightward Upward 1000fps
1000fps
Leftward
0˚
63˚
-28˚ (-30.5 ˚)
30˚ (31.5 ˚)
-62 ˚
1 ˚
-10 ˚ 10 ˚
0 ˚(0 ˚)

57. Steerable Jumping Robot
Upward
1000fps
10˚-15˚
-3˚(-2.5 ˚)
45˚
13˚ 27˚ (28 ˚)
1000fps
20˚
Added 20g mass
Proposed
mechanism
Added mass
Servo motor 1.8 g 1.8 g
Leg 3.2 g -
Added mass - 20.0 g
1000fps
Rightward

58. A Multi-Modal
Jumping-Crawling Robot

59. Increasing Ability to Move
Speed (Body length/sec)
0.3
0.16
0.33
9.0
20.0
30.05.0
Honda Asimo
Humanoid
Stickybot (2006) S Hirose (2005)
Snake robot
DASH (2009),
UC Berkeley Automobile
Integrated Jumping-Crawling
Obstacle size (cm)
150.0

60. Trajectory-Adjustable Jumping-Crawling Robot
Fast crawl + Low jump Slow crawl + High jump Slow crawl + Low jump
Control both speeds in x and y direction for practical use

61. Integrated JumpRoACH
Components Mass (g)
Jumper 40
Shell 11
Crawler 33
Battery 7
Control board 8
Total 99 Jumper
Crawler
Shell
Self-right and Go
X 1.7

62. Large Energy Storage
• Jump over 1.5m with 100g
• More than 1.6 J
Compressible Structure
• 2cm (height) x 2cm (width) x 10cm (length)
• Robustness to high compression load
Energy Releasing Mechanism
• Height-adjustable trigger mechanism
• Energy releasing without time delay
Requirements on Jumping Mechanism
10cm
5cm
DASH (30g, 1.5 m/s), UC berkeley

63. Issues on milli-scale jumping
mechanism
Increasing Energy-Storing Capacity

64. Current Milli-Scale Jumping Mechanisms
Energy density
[mJ/g]
Size [m]
7g jumping robot
D. Floreano et al. 2008
MSU Jumper
J. Zhao et al. 2012
0
20
30
0.01 0.1
Grillo
P. Dario et al. 2008
FLEA robot
K. Cho et al. 2012
Proposed
mechanism
10
Closed Elastica
A. Amada et al. 2008

65. Maximizing Displacement of Elastic Component
Maximizing energy storage
k/3, 3x k, x
Assumption:
- both structures has equal loading force limit,
𝑆𝑡𝑜𝑟𝑒𝑑 𝐸𝑛𝑒𝑟𝑔𝑦 =
3
2
𝑘𝑥2 𝑆𝑡𝑜𝑟𝑒𝑑 𝐸𝑛𝑒𝑟𝑔𝑦 =
1
2
𝑘𝑥2
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑆𝑡𝑜𝑟𝑒𝑑 𝐸𝑛𝑒𝑟𝑔𝑦
=
1
2
𝑛𝑘𝑥2
, 𝑤ℎ𝑒𝑛 𝑎 𝑠𝑝𝑟𝑖𝑛𝑔 ℎ𝑎𝑠 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑒 𝑜𝑓
𝑘
𝑛
𝑎𝑛𝑑 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑛𝑥
𝑆𝑡𝑜𝑟𝑒𝑑 𝐸𝑛𝑒𝑟𝑔𝑦 ∝ 𝑘, 𝑥2
𝐹 = 𝑘𝑥.

66. Material selection
Ashby, “Materials Selection in Mechanical Design”, 1992
Materials for efficient light springs
Materials
Ml = 𝜎𝑓
2
/𝜌𝐸
(kJ/kg)
Comment
Ti alloys 4-12 Better than steel; corrosion-resistant; expensive
CFRP 6-10 Better than steel; expensive
GFRP 1.0-1.8 Better than spring steel; less expensive than CFRP
Spring steel 3-7 Poor, because of high density
Wood 0.3-0.7 On a weight basis, wood makes good springs
Nylon 1.5-2.5 As good as steel, but with a high loss factor
Rubber 20-50 Outstanding; 20 times better than spring steel but with high loss factor
1st prototype, 10g,
1.5m jump with 50g payload
2nd prototype, 10g,
1.2m jump with 50g payload
3nd prototype, 10g,
1.2m jump without payload
4th prototype, 10g,
4m jump with 50g payload
Latex rubber Pre-strained Carbon Strap Spring steel Carbon beam

67. Loading Force Analysis
𝑟𝐹𝑠𝑖𝑛𝜃
= 𝑟1 𝑘1 𝛥𝑥1 𝑐𝑜𝑠𝜃 + 𝑟2 𝑘2 𝛥𝑥2 𝑐𝑜𝑠𝜃 + 𝑟3 𝑘3 𝛥𝑥3 𝑐𝑜𝑠𝜃
𝛥𝑥𝑖 = 𝑟𝑖(𝑠𝑖𝑛𝜃 − 𝑠𝑖𝑛𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ,
𝐹
=
8 𝑘1 𝑟1
2
+ 𝑘2 𝑟2
2
+ 𝑘3 𝑟3
2
𝑠𝑖𝑛𝜃 − 𝑠𝑖𝑛𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑠𝜃
𝑟 𝑠𝑖𝑛𝜃
From moment equilibrium,
where
Therefore,
𝜃′
= 𝜃/2
𝐸 = 2(
1
2
𝑘1∆𝑥1
2
+
1
2
𝑘2∆𝑥2
2
+
1
2
𝑘3∆𝑥3
2

68. Loading Force Analysis
where 𝑟1 = 41𝑚𝑚, 𝑟2 = 36𝑚𝑚, , 𝑟3 = 31𝑚𝑚, 𝑟 =
45𝑚𝑚 , 𝑘1 = 86.43𝑁/𝑚 , 𝑘2 = 100.07𝑁/𝑚 , 𝑘3 =
108.25𝑁/𝑚 and 𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 20
Motor stall torque, τ = 0.9 Nm
∴ 𝑃𝑢𝑙𝑙𝑒𝑦_𝑟𝑎𝑑𝑖𝑢𝑠 𝑚𝑎𝑥= τ/𝐹𝑝𝑒𝑎𝑘 = 12 𝑚𝑚
Storable energy = 1.39 J
Failure

69. Limited Structural RobustnessLoadingForce
Displacement
Limit of Structural Robustness
linear spring torsion spring
Linear + torsion
Loading Force vs. Types of Energy Storage

70. Types of Energy Storage
Linear spring Torsional spring
𝑟𝐹𝑠𝑖𝑛𝜃 = (𝑟1 𝑘1 𝛥𝑥1 + 𝑟2 𝑘2 𝛥𝑥2 + 𝑟3 𝑘3 𝛥𝑥3 𝑐𝑜𝑠𝜃 + 𝑘t 𝛥𝜃
Loading Torque
𝐹 = 𝑟1 𝑘1 𝛥𝑥1 + 𝑟2 𝑘2 𝛥𝑥2 + 𝑟3 𝑘3 𝛥𝑥3 𝑐𝑜𝑠𝜃/𝑟𝑠𝑖𝑛𝜃 + 𝑘t 𝛥𝜃/𝑟𝑠𝑖𝑛𝜃
Loading Force
linear spring torsional spring
Linear
only
Torsion
only
Peak Force
limit
40 N 40 N
Stored
Energy
1.38 J 1.98 J

71. Peak Loading Force
Condition: 40N Structual Limit
2.31 J
1.9 J in torsion spring
0.41 J in linear spring
1.98 J
1.38 J

72. Issues on milli-scale jumping
mechanism
Fully Compressible Robust Joint

73. Current Milli-Scale Jumping Robots
Types of
Joint
Range of Motion
(Energy Storage Capacity)
Compression Load
Bearing Ability
(Structure Robustness)
Stored
Energy
Compact
ness
Friction
Low
(50˚ ~ 180˚)
High
(depends on shaft dia.,
joint material)
0.34 J
(23.5 g,
0.87 m)
Low
(pin thickness,
hosing) High
(bearing
required)
High
(0˚ ~ 180˚)
Low
(~2N)
0.067 J
(2.25 g,
1.2 m)
High
Low
High
(0˚ ~ 180˚)
Med
(depends on flexure and
wire material properties)
1.4 J
(38.4 g,
3 m)
Med Low
Pin Joint
J. Zhao et al. 2012
Flexure Joint
J. Koh et al. 2013
180˚
0˚
Rolling Joint
180˚
0˚
180˚
50˚
Joints in Milli-Scale Jumping Robots

74. Knee-inspired Cross-axis Rolling Joint
Wire + Cross fiber Wire only
Joint Operation
- Rolling joint
- High range of motion (almost 0˚~180˚)
- Simple structure (two rigid beams + fabric)
Loading
Human Knee
E. Pena et al., 2005
- Robust to high compression force.
- Crucial ligament prevents off-axis movement

75. Requirements on Joint
- Required Range of Motion:
0˚ ~ 180˚
𝐹comp𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = 4 (𝑟1 𝑘1 𝛥𝑥1 + 𝑟2 𝑘2 𝛥𝑥2 + 𝑟3 𝑘3 𝛥𝑥3 𝑐𝑜𝑠𝜃=77 N
𝛥𝑥𝑖 = 𝑟𝑖(𝑠𝑖𝑛𝜃 − 𝑠𝑖𝑛𝜃𝑖𝑛𝑖𝑡𝑖𝑎𝑙where
Wide range of motion
- Required Load Bearing Capacity: More than 77 N compression load
Robustness to compression
Robustness to off-axis load
- Off-axis load in the worst case: 28.3 N
𝐹off−axis = 2 (𝑟1 𝑘1 𝛥𝑥1 + 𝑟2 𝑘2 𝛥𝑥2 + 𝑟3 𝑘3 𝛥𝑥3

76. Issues on milli-scale jumping
mechanism
Height-adjustable Triggering Mechanism

77. Trigger Mechanisms in Milli-scale Jumping Robots
Leornardo da Vinci.
7g jumping robot
M. Kovac et al. 2008
MSU Jumper
J. Zhao et al. 2012
Gradual storage + Fast release
Escapement-Cam based Catapult Mechanism
- Store fixed amount of energy, Hard to adjust trigger timing
Flea-inspired Jumping Mechanism
M. Noh et al. 2012 Multimo-Bat
M. A. Woodward et al. 2014
Active clutch using SMA wire
Active trigger using multiple actuators
- Active Clutch
- Need at least two actuators
(one for store, one for release)
Active trigger using SMA spring

78. Height-adjustable Jumping
Store the elastic energy in latex rubber.
Store the elastic energy in latex rubber.
Stored energy can be released in any shape.

79. Active and Height-adjustable Trigger
MOTOR
clockwise counter clockwise
: Planet gear
: Winding gear
: Actuating gear
Active Releasing based on a single DC motor
Inspiration from planetary gear
: Releasing
: Winding
Winding Self-locking Releasing

80. Removing Undercut
TRelease
TRelease
FPM
FPM
Pressure angle 0 deg. Pressure angle 60 deg.
Pressure Angle of Involute Shape Gear
Rack cutting Hobbing
Undercut starts to occur as the number
of tooth decreases.
20˚ pressure angle, the minimum number
of tooth is 18.

81. Releasing without Delay
Force Analysis
FPM
FPM,t
FPM,n
FPW
FPW,t
FPW,n
𝛼0
𝛼0
′
𝑭 𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏
Friction force induced by FPW,t : 𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝜇𝐹𝑃𝑊 𝑐𝑜𝑠𝛼0
𝛼0 = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑛𝑔𝑙𝑒 between planet gear and widing gear
𝜇 = 𝑓𝑟𝑖𝑐𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 (0.7
𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 < 𝐹𝑃𝑊 𝑠𝑖𝑛𝛼0 + 𝐹𝑃𝑀 𝑐𝑜𝑠𝛼0
′
According to the condition,
𝛼0
′
= 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑛𝑔𝑙𝑒 𝑏𝑒𝑡𝑤𝑤𝑒𝑛 𝑝𝑙𝑎𝑛𝑒𝑡 𝑔𝑒𝑎𝑟 𝑎𝑛𝑑 𝑚𝑜𝑡𝑜𝑟 𝑔𝑒𝑎𝑟 (20˚
Friction induced by FPW,t < FPW,n + FPM,t
𝜇𝑐𝑜𝑠𝛼0, 𝑚𝑖𝑛 − 𝑠𝑖𝑛𝛼0,𝑚𝑖𝑛 =
𝐹𝑃𝑀
𝐹𝑃𝑊
𝑐𝑜𝑠𝛼0
′
The minimum pressure angle of winding gear is given as:
Following condition should be satisfied:
𝛼0, 𝑚𝑖𝑛 = 27˚
Releasing

82. Results
Removing Delay using a Gear with pressure angle of 30˚
Releasing
Fast release Delayed release
Conditions for Removing Delay
- Low friction (𝛼0, 𝑚𝑖𝑛 = 27˚)
- Inter-locking induced by tooth shape (𝛼0, 𝑚𝑖𝑛 = 21˚)

83. Dynamics & Experimental Results

84. Combined Energy Storages
Components Mass (g)
Jumper Transmission 4.6
Motor case 1.1
Motor 12.0
Joints (8ea) 4.0
Wire, joint rubber 2.2
Carbon rods (8ea) 2.0
latex rubber (2 ea) 2.0
Control board 1.0
Li-Po Battery 2.5
Torsion spring (12ea) 6.2
Torsion spring axis (4ea) 1.3
Total 42.6
torsion springs
linear springs
rolling joints
RF receiver
Li-Po battery
DC motor
loading wire
torsion springs
9.5 cm
2.5 cm
Active clutch

85. Dynamics
Lagrangian Formulation
- Take-off velocity
- Take-off time
- Acceleration
- Reaction force
- Actual used energy
Take-off (Reaction Force = 0)

86. Experimental Results
Torsion spring only
Combined case
Torsion spring only Combined
Exp. Sim. Exp. Sim.
Stored Energy (J) 1.39 1.39 1.81 1.81
Take-off time (ms) 15.0 13.9 14.0 12.6
Take-off speed
(m/s)
6.9 6.98 7.83 8.09
*Conversion
efficiency (%)
66.3 69.7 67.2 70.9
*conversion efficiency is a ratio of initially stored energy
to actually used energy for jumping
2000fps
2000fps

87. Experimental Results
2.4m
3.0 m
Torsional spring only Combined
Torsion
spring only
Combined
Stored Energy (J) 1.39 1.81
Stored Energy in
torsion spring (J)
1.39 1.39
Stored Energy in
linear spring (J)
0 0.42
Take-off speed (m/s) 6.9 7.83

88. Bio-inspiration
Novel Mechanism Design Kinematic & Dynamic Analysis
Take advantage of the softness/compliance
of the structure
ex) Asymmetricity, Bistability, Buckling, Patterning
Understand how the dynamic system
works
ex) Acceleration, Reaction force, Energy
distribution
 Caterpillar-inspired gripper based on flexural
buckling
 Froghopper-inspired direction changing
concept
 Flea-inspired jumping mechanism
Application to Robotic System
 Buckling hand
 Wheel Transformer
 Integrated Jumping-Crawling

89. Thank You