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HOW TO MODIFY LINK STIFFNESS TO ACHIEVE CONTROLLABLE LINEAR MOTION OF A ROBOTIC ACTUATOR/S USING FOLDABLE ROBOTICS TECHNIQUES

EGR 557

TEAM 7

Claudio Vignola

Chien-Wen Pan

Dallas Wells

Manoj Akkaraboina

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CURRENT SPECIFICATIONS

Parameter Old	Value Range Old	Unit	Informed Value	Current Value	Reference
Length of Whole body	175	mm	Length of Top Bar	180	[1]
Mass of Whole body	100	g	Mass of Structure	45	[1]
Mass of the Jaw	2	g	Mass of 4 Bar Mechanism	12.8	[1]
Jaw Reaching Distance	30 - 45	mm	Reaching Distance	155	[2]
Time to reach prey	28 - 40	msec	Time of End Effector Max Reach	40	[2]
Time to Jaw Retraction	102 - 120	msec	Time for Retraction	500	[2]
Max Protrusion Velocity	1.86 - 2.76	m/sec	Max Velocity	0.6425	[2]
Max Protrusion Acceleration	67.4 - 155	m/sec^2	Acceleration	0.257	[2]
Mass of movable object	20	g	End Effector Grasp Force	Unknown	[3]

Materials	Cost $	Reason
Cardstock	4.97	First Prototyped Model, Might be used as a bend for storing energy
Cardboard	1.48	Stiffening 1A,1B,1C, and 1D for second Model
Super Glue	3.47	Connection between links
Orange Spring	Free	Relative low energy metal spring
Yellow Spring	Free	Longer and stronger metal spring compared to Yellow
Total	9.92

Spring	K Constant (N/m)	Initial Spring Lenght (cm)	Max Spring Length (cm)
Orange Spring	413.6	10.44	11.13
Yellow Spring	591.29	13.1	15.24
Cardstock Single	15	11.0	11.0
Cardstock Double	30	11.0	11.0

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DYNAMICS

Add a spring with changeable location to study how it affects the behavior of the device.
Use a leaf spring to model the compliant beam.
Servo motor pulls back the device but there’s no propelling purpose.

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DATA COLLECTION, PARAMETER IDENTIFICATION, AND MODEL FITTING

Mass & Inertia Modeling

A Solidworks CAD Model was made of each link of the assembly. Using density found from weighing material samples, the center of mass and inertia were modeled using the Mass Properties tool on the part file of each link..

Beam Stiffness Modeling

To model stiffness of link materials, 4 samples of a given material were obtained, and pictures of deflection from a given force were taken.
These pictures were then uploaded into a MATLAB image processing tool, and a pixel measurement of the 1cm background grid was used to scale. Then measurements were taken for deflection, and plotted against force.
A linear regression was applied to each and averaged to determine the Young’s Modulus, and with the E the beam stiffness was computed.
The model was then compared to a Solidworks deformation simulation for validation.
The process was then repeated for each link material.

Spring Modeling

To model the spring constants, weights were attached to the springs used vertically and the deflection was measured. The constant was then determined with a linear fit the experimental data.

Damper Modeling

In order to determine the damping in the system, we used the dynamic model in pynamics to tune the oscillating characteristics.

Compliant Link Modeling

To use the compliant link driving our mechanism within the Pynamics model, the link was approximated as two separate links joined by a spring. The spring constant was determined from the material stiffness.
The link lengths were determined empirically from the maximum bending location of the prototype within Tracker from slow motion videos.

We primarily needed to model six parameters in our system, center of mass and moments of inertia for each link, the spring constants for the springs used, the damping within the system,

the stiffness of links, and the placement of the spring representing our compliant link. The motor parameters were not modeled as in our design the motor is only used to reset the device,

so it doesn't affect the dynamic characteristics.

To model the mass and inertial properties, a CAD model was made in Solidworks shown below. To determine the density of our materials, material samples of a specific volume

were weighed and averaged, and the result was input into Solidworks material model. From there the center of mass and inertias for each link was determined with the Mass Properties tool.

The sping constants were modeled empirically by hanging a series of weights vertically from the spring and measuring the deflection. This data was then plotted, and a linear fit applied to

determine the spring constants.

Instead of modeling the damping of the system, the dynamics model was used to determine the optimal damping needed. The pynamics model was run with varied damping constants and

the values that produced the satisfactory oscillation behavior were chosen.

The stiffness of the materials was modeled by measuring the deflection of material samples through pictures such as the one seen to the right, and a MATLAB image processing tool.

The 1cm grid scale was measured in pixels and used to normalize the measurements. These defection vs force curves were then plotted and a linear regression was applied, shown in the graph

to the right. The slope from the regression was then used to determine the Young's Modulus and the stiffness coefficient. These values were then added to the Solidworks materials

and verified using a simulation as seen here.

To model the compliant link driving our system, the link was split into two separate links combined by a leaf spring. To determine the position of the leaf spring, several slow motion videos were

taken of the prototype models. The bending of these models were then tracked in the Tracker program, and the location of maximum bending was chosen to separate the link at.

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FUTURE PLANS

Identify a pressure sensor for the end effector.
Actuate the gripper.
Stiffness study- Impact of stiffness on:

a) Locomotion of the robotic arm.

b) Safety during human interaction.

c) Energy efficiency of the robotic system with change in stiffness.

Rigid body movement vs external load.
Stiffness change with change in length of robotic arm.
Stiffness study for robotic arms with different materials.
Limitations.

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References

S. Burgess, J. Wang, A. Etoundi, R. Vaidyanathan and J. Oliver, "A functional analysis of the jaw mechanism in the sling-jaw wrasse", International Journal of Design & Nature and Ecodynamics, vol. 6, no. 4, pp. 258-271, 2011. Available: 10.2495/dne-v6-n4-258-271.
M. Westneat and P. Wainwright, "Feeding mechanism of Epibulus insidiator (Labridae; Teleostei): Evolution of a novel functional system", Journal of Morphology, vol. 202, no. 2, pp. 129-150, 1989. Available: 10.1002/jmor.1052020202.
M. Strawberry and T. Cohent, "How Many Strawberries in a Serving? (Helpful Table)", Strawberry Plants . org, 2021. [Online]. Available: https://strawberryplants.org/strawberry-serving/. [Accessed: 22- Mar- 2021].