This paper presents the design and development of a new
type of piezoelectric-driven robot, which consists of a piezoelectric
unimorph actuator integrated as part of the structure of a
four-bar linkage to generate locomotion. The unimorph actuator
replaces the input link of the four-bar linkage and motion is generated
at the coupler link due to the actuator deflection. A dimensional
synthesis approach is proposed for the design of four-bar
linkage that amplifies the small displacement of the piezoelectric
actuator at the coupler link. The robot consists of two such
piezo-driven four-bar linkages and its gait cycle is described. The
robot speed is derived through kinematic modelling and experimentally
verified using a fabricated prototype. This result will be
important for developing a motion planning control strategy for
the robot locomotion, which will be part of future work.
FEA Based Level 3 Assessment of Deformed Tanks with Fluid Induced Loads
Design and Gait Analysis of a Two-legged Miniature Robot with Piezoelectric-driven Four-bar Linkage
1. 1
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus DharmawanDesign and Gait Analysis of a
Two-legged Miniature Robot with
Piezoelectric-driven Four-bar Linkage
Audelia G. Dharmawan, Hassan H. Hariri, Gim Song Soh, Shaohui Foong,
and Kristin L. Wood
2. 2
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Introduction
Miniature
mobile
robots
Light weight,
small size
Swarming and
distributed sensing
Tight spaces
inaccessible
by human
Dharmawan et al., 2017 Son et al., 2006
Ho et al., 2009
Rios et al., 2017 Baisch, 2013
Avirovik et al., 2014
Piezoelectric
Actuator
Image from http://www.militaryaerospace.com
Image from http://www.militaryaerospace.com Image from http://blog.ascens-ist.eu
3. 3
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Problem
Limited displacement of
piezoelectric actuator
Amplification through linkage
mechanism to achieve larger stroke
Some linkage mechanism
Adapted from Sahai, 2006
4. 4
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Literature Review
Common approach of choosing the geometric parameters of the linkages:
• Arbitrarily
• Optimization
No technique exists for a task-oriented design of piezo-driven mechanism that achieves a
required stroke amplification or gait trajectory
Multiple four bar Five bar Spherical five bar
Sitti, 2003 Goldfarb et al., 2001
Baisch et al., 2010
5. 5
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Objective
• Formulate a design methodology for
selecting parameters for the design of
piezo-driven legged robots through the
use of 4-bar linkages.
6. 6
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Outline
Dimensional
Synthesis
• Joint limit
identification
• Design for stroke
amplification
Gait Analysis
• Gait cycle modeling
• Mathematical
modeling of robot
motion
Experimental
Verification
• Robot prototype
• Experimental
Results
Dimensional Synthesis Gait Analysis Experimental Verification
7. 7
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Unimorph Actuator
Dimensional Synthesis Gait Analysis Experimental Verification
8. 8
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Dimensional Synthesis
Restriction:
• Actuator length
• Actuator displacement
Requirement:
• Amplification factor
Dimensional Synthesis Gait Analysis Experimental Verification
9. 9
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Joint Limit Identification
• Equation of motion (Hariri et al., 2011):
(𝐸𝐼) 𝑒𝑞
𝜕2
𝑤(𝑥)
𝜕𝑥2
= −𝑞𝑒 𝑝 𝐸𝑧
• With fixed-free boundary conditions,
displacement:
𝑤 𝑥 =
−𝑞𝑒 𝑝 𝐸𝑧
2(𝐸𝐼) 𝑒𝑞
𝑥2
• Angular displacement:
ζ ≈
𝑤(𝑙)
𝑙
• Joint limits:
𝜃1,𝑚𝑖𝑛 = 𝜃1,0 − ζ
𝜃1,𝑚𝑎𝑥 = 𝜃1,0 + ζ
Dimensional Synthesis Gait Analysis Experimental Verification
𝜃1,𝑚𝑖𝑛
𝜃1,𝑚𝑎𝑥
10. 10
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Design for Amplification
• Introduce a stroke amplification (𝛼):
𝜃2,𝑚𝑖𝑛 = 𝜃2,0 − 𝛼ζ
𝜃2,𝑚𝑎𝑥 = 𝜃2,0 + 𝛼ζ
• Choose five task positions from this range for the synthesis of four-bar linkage:
𝑇 = 𝐺 𝑍(𝜃1) 𝑋(𝑎) 𝑍(𝜃2) [𝐻]
Dimensional Synthesis Gait Analysis Experimental Verification
𝜃1,𝑚𝑖𝑛
𝜃1,𝑚𝑎𝑥
𝜃2,𝑚𝑖𝑛
𝜃2,𝑚𝑎𝑥
11. 11
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Outline
Dimensional
Synthesis
• Joint limit
identification
• Design for stroke
amplification
Gait Analysis
• Gait cycle modeling
• Mathematical
modeling of robot
motion
Experimental
Verification
• Robot prototype
• Experimental
Results
Dimensional Synthesis Gait Analysis Experimental Verification
12. 12
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Gait Cycle Model
Dimensional Synthesis Gait Analysis Experimental Verification
High Speed Camera @ 12.5 KHz
13. 13
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Gait Cycle Model
Front Leg Stance Back Leg Stance
Dimensional Synthesis Gait Analysis Experimental Verification
17. 17
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Outline
Dimensional
Synthesis
• Joint limit
identification
• Design for stroke
amplification
Gait Analysis
• Gait cycle modeling
• Mathematical
modeling of robot
motion
Experimental
Verification
• Robot prototype
• Experimental
Results
Dimensional Synthesis Gait Analysis Experimental Verification
18. 18
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Robot Prototype
Dimensional Synthesis Results
Properties of the Unimorph Actuator
• Dimension: 100 x 17.4 x 27.2 mm
• Mass = 12.17 g
Dimensional Synthesis Gait Analysis Experimental Verification
19. 19
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Experimental Results
Dimensional Synthesis Gait Analysis Experimental Verification
20. 20
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Conclusion
• Propose a design methodology for selecting parameters for the design of piezo-driven robots
• Perform gait and kinematic analysis to predict the motion of the robot
• Fabricate a prototype of the robot and conduct experimental test
Dimensional
Synthesis
• Joint limit
identification
• Design for stroke
amplification
Gait Analysis
• Gait cycle modeling
• Mathematical
modeling of robot
motion
Experimental
Verification
• Robot prototype
• Experimental
Results
21. 21
Prof. Kevin Otto, Prof. Soh Gim Song, Prof. Foong Shaohui,
Hanson Chen Xiaohan, Blake William Clark Sedore, Audelia Gumarus Dharmawan
Future Work
Smolka et al., 2013