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# Mechanical design and fabrication of a kinetic sculpture with application to
bioinspired drone design

Andrew Lessieur  SiliconSynapse Laboratory at Northeastern University, Boston,
USA  Eric Sihite  SiliconSynapse Laboratory at Northeastern University,
Boston, USA  Pravin Dangol  SiliconSynapse Laboratory at Northeastern
University, Boston, USA  Akshath Singhal  SiliconSynapse Laboratory at
Northeastern University, Boston, USA  Alireza Ramezani  SiliconSynapse
Laboratory at Northeastern University, Boston, USA

###### Abstract

Biologically-inspired robots are a very interesting and difficult branch of
robotics dues to its very rich dynamical and morphological complexities. Among
them, flying animals, such as bats, have been among the most difficult to take
inspiration from as they exhibit complex wing articulation. We attempt to
capture several of the key degrees-of-freedom that are present in the natural
flapping gait of a bat. In this work, we present the mechanical design and
analysis of our flapping wing robot, the Aerobat, where we capture the
plunging and flexion-extension in the bat’s flapping modes. This robot
utilizes gears, cranks, and four-bar linkage mechanisms to actuate the arm-
wing structure composed of rigid and flexible components monolithically
fabricated using PolyJet 3D printing. The resulting robot exhibits wing
expansion and retraction during the downstroke and upstroke respectively which
minimizes the negative lift and results in a more efficient flapping gait.

###### keywords:

Robot design, aerial robot, bio-inspired robot

##  1 INTRODUCTION

The overall goal of this work is to advance the theory and practice of aerial
robots that are soft, agile, collision-tolerant, and energetically efficient
by the biomimicry of key airborne vertebrate flight characteristics. In recent
years, much attention has been drawn to make our residential and work spaces
smarter and to materialize the concept of smart cities [1]. As a result,
safety and security aspects are gaining ever growing importance [2] and drive
a lucrative market. Systems that can provide situational awareness to humans
in residential and work spaces or contribute to dynamic traffic control in
cities will result in large-scale intelligent systems with enormous societal
impact and economic benefit.

Current state-of-the-art solutions with rotary or fixed-wing features fall
short in addressing the challenges and pose extreme dangers to humans. Fixed
or rotary-wing systems are widely applied for surveillance and reconnaissance,
and there is a growing interest to add suites of on-board sensors to these
unmanned aerial systems (UAS) and use their aerial mobility to monitor and
detect hazardous situations in residential spaces. While, these systems, e.g.,
quadrotors, can demonstrate agile maneuvers and have demonstrated impressive
fault-tolerance in aggressive environments, quadrotors and other rotorcrafts
require a safe and collision-free task space for operation since they are not
collision-tolerant due to their rigid body structures. The incorporation of
soft and flexible materials into the design of such systems has become common
in recent years, yet, the demands for aerodynamic efficiency prohibit the use
of rotor blades or propellers made of extremely flexible materials.

The flight apparatus of birds and bats can offer invaluable insights into
novel micro aerial vehicle (MAV) designs that can safely operate within
residential spaces. The pronounced body articulation (morphing ability) of
these flyers is key to their unparalleled capabilities. These animals can
reduce the wing area during upstrokes and can extend it during downstrokes to
maximize positive lift generation [3]. It is known that some species of bats
can use differential inertial forces to perform agile zero-angular momentum
turns [4]. Biological studies suggest that the articulated musculoskeletal
system of animals can absorb impact forces therefore can enhance their
survivability in the event of a collision [5].

The objective of this paper is to design and develop a bio-inspired soft and
articulated armwing structure which will be an integral component of a
morphing aerial co-bot. In our design, we draw inspiration from bats. Bat
membranous wings possess unique functions [6] that make them a good example to
take inspiration from and transform current aerial drones. In contrast with
other flying vertebrates, bats have an extremely articulated musculoskeletal
system, key to their body impact-survivability and deliver an impressively
adaptive and multimodal locomotion behavior [7]. Bats exclusively use this
capability with structural flexibility to generate the controlled force
distribution on each wing membrane. The wing flexibility, complex wing
kinematics, and fast muscle actuation allow these creatures to change the body
configuration within a few tens of milliseconds. These characteristics are
crucial to the unrivaled agility of bats [8] and copying them can potentially
transform the state-of-the-art aerial drone design.

As part of our past work, we have developed a flapping wing robot mimicking
bat flight, the BatBot (B2) [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], which
incorporates a linkage mechanism to articulate plunging motion and wing
folding through mediolateral movements. In our most recent work, we have
developed a computational structure fabricated monolithically using soft and
rigid components [19, 20], as shown in Fig. 1. This structure, called the
Kinetic Sculpture (KS), was designed to capture bat dynamically versatile wing
conformations and mimic the soft and articulated armwing structure of bat
membraneous wing through mechanical intelligence.

##  2 ARMWING STRUCTURE DESIGN OVERVIEW

Figure 1: Illustration of Northeastern University’s Aerobat, which features a
kinetic sculpture capturing the dynamic wing morphing of bats. The wing
membrane is made out of flexible PCB which carries sensors, motor drivers,
communication unit, and a microcontroller.

The Northeastern University’s Aerobat, shown in Fig. 1, is a flapping wing
robot with a maximum wingspan of 30 cm. This robot is designed for evaluating
the flapping performance of the KS shown in Fig. 1. This design shows that we
are capable of animating dynamic wing morphing seen in bats. The KS design
iterations and robot design will be discussed in more detail in this section.

The Aerobat is designed to show the feasibility of untethered flight using the
KS we designed in Section 2.1. In this prototype, the KS is implemented using
using rigid linkages and joints fabricated out of acrylic lasercut components
and metal hinges. This linkage structure is capable of articulating our
desired wing folding and expansion, as shown in Fig. 2. The body and several
other mounting components, such as spacers, were fabricated out of 3D printed
plastic.

We designed the wing membrane using flexible PCB, shown in Fig. 1, where we
attach sensors, motor drivers, communication modules, and microcontroller
unit. The components attached on the wings will be used as a part of our
future work to incorporate mechanical intelligence to facilitate control in
this robot. In this framework, we utilize several small and low power
actuators, called the Feedback Driven Components (FDC), to adjust the KS
conformations. By attaching these FDCs on a highly sensitive KS component, we
can significantly change the resulting flapping trajectory through a small
adjustment in KS conformation. This allow us to adjust the resulting
aerodynamic forces and facilitate control to stabilize the robot’s attitude.
our robot is pitch unstable which is what we expected in a tail-less
ornithopthers, which makes active or passive stabilizer necessary in this
robot.

The KS of both wings are coupled using 7 spur gears, allowing us to actuate
them using a single electro-magnetic actuator. We selected the fastest and
lightest brushless motor with a gearbox reduction ratio of 75:1 that is
capable of providing enough speed and torque to fully actuate the KS at high
flapping speed.

Figure 2: The time-lapsed images of the bat armwing articulation. Images 1-2
show the wing downstroke/expansion motion while images 3-4 show the wing
upstroke/retraction motion. The armwing is monolithically fabricated using
both rigid and flexible materials in a PolyJet 3D printer.

###  2.1 Kinetic Sculpture Design

We designed our KS using flexible and rigid materials monolithically
fabricated using PolyJet 3D printing [19]. The KS utilized a series of four-
bar mechanisms (mechanical amplifiers) to animate the wing plunging motion in
addition to the wing folding and expansion. We designed the driving mechanism
such that both wings can be actuated by a single motor through the use of spur
gears and crank mechanisms.

We used the PolyJet flexible materials for the monolithic fabrication process.
These materials come in Shore hardness scale range of 30A to 85A which is
formed by mixing the rigid Vero White and the flexible Agilus Black. The
design variations for compliant joints outlined in [21] were considered where
they vary in size, off-axis stiffness, axis drift, stress concentration, and
range of motion.

We picked a combination of 1.3 and 2mm thick flexible hinges and the flexible
materials [22] shown in Table 1. The larger cross-sectional areas improve the
durability and the off-axis stiffness of the joints, but also increased the
overall weight of the KS. We found out that the KS with durometer scale of 50A
is too soft to be used in the wing articulation and it has very little off-
plane and torsional stiffness even in the thicker hinge design. On the other
hand, the KS with durometer scale of 85A and 2mm hinge thickness is too stiff
and brittle. Out of all the combinations we tested, we found that the KS with
70A durometer and 1.3 mm hinge thickness have the best overall result in the
wing articulation and stiffness.

Table 1: Table of the Tested Hinge Materials Material | Shore Hardness (A) | Elongation at Break (%)
---|---|---
FLX 9850 | 50 - 55 | 170 - 210
FLX 9870 | 60 - 70 | 120 - 140
FLX 9885 | 80 - 85 | 70 - 90

###  2.2 Armwing Optimization

The ideal flapping motion that we are looking for has the following
properties: (1) the wing extends and retracts during downstroke and upstroke
respectively, (2) the wing is already partially expanded before the downstroke
motion begins. The desired shoulder and elbow trajectories ($\hat{\theta}_{s}$
and $\hat{\theta}_{e}$, respectively) can be seen in Fig. 3b, which are
defined as the following sinusoidal functions

$\begin{gathered}\hat{\theta}_{s}=35^{\circ}\,\sin(\phi)-10^{\circ}\\\
\hat{\theta}_{e}=-0.5\,\tan^{-1}\left(\tfrac{-0.5\,\sin(\phi+2\pi/3)}{1+0.5\,\cos(\phi+2\pi/3)}\right)\,45^{\circ}+120^{\circ},\end{gathered}$
(1)

where $\phi\in[0,2\pi)$. $\hat{\theta}_{e}$ is a skewed sinusoidal function
which allows the wing to expands faster than the retraction and have a full
wingspan in the middle of the downstroke.

The design optimization will solve for some of the mechanism design parameters
using our initial mechanism design in Solidworks for the initial conformation
parameter $\bm{q}$. There are 38 parameters in the design space of this
armwing and we constrain some of these parameters to fit our design criterion
and reduce the search space of the optimizer. In order to have a symmetric
gait between the left and right wing, the drive gears must be centered and the
crank arm maximum horizontal length must be aligned with the body $y$ axis.
Additionally, we fix the values for the gear positions and the length of
humerus and radius linkages. This leaves us with 30 design parameters to
optimize.

Considering the large design space of this wing structure, solving for all 30
parameters at the same time is not practical due to the large computational
time and search space. The radius mechanism must follow a trajectory in
relation to the humerus mechanism to articulate the appropriate elbow angle.
Therefore, we can separately optimize the humerus and radius mechanisms,
starting from the humerus mechanism. The humerus and radius mechanisms have 13
and 17 design parameters, respectively.

The optimization problem can be formulated as

$\displaystyle\min_{\bm{q}}$ $\displaystyle(\bm{y}^{T}\,\bm{y})/N$ (2) subject
to: $\displaystyle\bm{q}_{min}\leq\bm{q}\leq\bm{q}_{max},\quad\bm{f}_{c}\leq
0,$

where the the cost function is the mean squared value of $\bm{y}$ which is the
difference between target vs. the simulated trajectory, $N$ is the data size,
$\bm{q}$ is the parameter to optimize, $\bm{q}_{min}$ and $\bm{q}_{max}$ are
the parameter bounds, and $\bm{f}_{c}$ is the constraint function. We used the
interior-point method as the optimization algorithm in Matlab which has
successfully found a solution that matches the target trajectory well, as
shown in Fig. 3.

(a) Unoptimized armwing angles.

(b) Optimized armwing angles vs. target trajectories.

Figure 3: The unoptimized and optimized armwing shoulder and elbow angles
within a single wingbeat. The optimization has successfully found the
parameters that results in close tracking to the target trajectory.

###  2.3 Sensitivity Analysis

A considerable displacement can occur at the KS joints under high dynamic
loads, therefore it is crucial to analyze the effects of the joints
displacements to the resulting flapping trajectory. We evaluated this using
kinematics sensitivity analyses where we evaluating how a small change in
conformation parameters lead to a change in the resulting trajectory, as shown
in Fig. 4. The green and red lines represent an 2.5% increase and decrease
compared to the original parameter value, respectively. Highly sensitive
parameters, such as Fig. 4b and Fig. 4c, can greatly influence the resulting
flapping trajectory from a very small change in conformation.

(a) Adjustment to $l_{1}$ length.

(b) Adjustment to $l_{4}$ length.

(c) Adjustment to $l_{9}$ length.

Figure 4: Armwing elbow joint and wingtip trajectories generated by varying
one of the design parameter. The parameter is varied between 90% and 110% of
its original values. The green and red trajectory colors indicate larger and
smaller parameter values, respectively. Highly sensitive parameters such as
case (b) and (c) lead to a huge change in the resulting flapping trajectory.

###  2.4 Structural Analysis

We performed FEA in order to analyze the structural properties of the KS under
load and simulate the material bending during KS articulation. The FEA was
done using Solidworks Simulation where we subjected the input arms of the KS
with some load and analyzed the resulting deformation and stress distribution
within the KS. We simulated the elastic material in the KS using the material
property of FLX9870 (Table 1) which has the density of 1.15 g/cm3 and average
tensile strength of 5 MPa [22]. The simulation is done with the hyperelastic
Mooney-Rivlin model using the material constants of a rubber shown in [23],
with a Poisson’s ratio of 0.4999, and first and second material constants of
0.3339 Mpa and -0.337 kPa, respectively.

We simulated the deformations during the beginning of downstroke and upstroke
which is timing where the KS switches direction. As shown in Fig. 5, the
maximum strain during these two motions are 43% and 30%, respectively. This is
well under the maximum elongation at break of 120-140% for this material which
is sufficient to deal with unforeseen strain due to dynamic load and off-plane
perturbations.

(a) Wing expansion before the downstroke.

(b) Wing retraction before the upstroke.

Figure 5: FEA of the compliant mechanism under static torques acting on the
crank arms. The strain values are shown at the right side.

##  3 CONCLUSIONS AND FUTURE WORK

We present a novel bio-inspired monolithic bat armwing structure with both
flexible and rigid materials. This armwing structure is designed to expand and
retract during the wing flapping motion to maximize the net lift produced by
the wing. We also presented structural and sensitivity analysis of the armwing
structure to show the feasibility of using the flexible polyjet material under
dynamic load and the sensitive parameters in the mechanism. These sensitive
parameters can be exploited where we can incorporate morphological computation
where a simple control action can influence and achieve complex manipulation
in the body morphology which is commonly seen in nature [24]. A small change
in a sensitive conformation parameter can result a large change in flapping
trajectory which affects the resulting aerodynamic forces. This can be used in
a feedback stabilization controller which we will have to incorporate in the
system due to the inherent pitch instability of a tail-less ornithopter such
as Aerobat.

## References

  * [1] Everaerts, J. et al., “The use of unmanned aerial vehicles (uavs) for remote sensing and mapping,” The Int. Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 37(2008), 1187–1192 (2008).
  * [2] Pavlidis, I., Morellas, V., Tsiamyrtzis, P., and Harp, S., “Urban surveillance systems: from the laboratory to the commercial world,” Proceedings of the IEEE 89(10), 1478–1497 (2001).
  * [3] Tobalske, B. W., “Biomechanics and physiology of gait selection in flying birds,” Physiological and Biochemical Zoology 73(6), 736–750 (2000).
  * [4] Riskin, D. K., Bergou, A., Breuer, K. S., and Swartz, S. M., “Upstroke wing flexion and the inertial cost of bat flight,” Proc. of the Royal Society B: Biological Sciences 279(1740), 2945–2950 (2012).
  * [5] Roberts, T. J. and Konow, N., “How tendons buffer energy dissipation by muscle,” Exercise and sport sciences reviews 41(4), 186–193 (2013).
  * [6] Tanaka, H., Okada, H., Shimasue, Y., and Liu, H., “Flexible flapping wings with self-organized microwrinkles,” Bioinspiration & biomimetics 10(4) (2015).  doi: 10.1088/1748-3190/10/4/046005.
  * [7] Riskin, D. K., Willis, D. J., Iriarte-Díaz, J., Hedrick, T. L., Kostandov, M., Chen, J., Laidlaw, D. H., Breuer, K. S., and Swartz, S. M., “Quantifying the complexity of bat wing kinematics,” Journal of theoretical biology 254(3), 604–615 (2008).
  * [8] Azuma, A., [The biokinetics of flying and swimming ], American Institute of Aeronautics and Astronautics (2006).
  * [9] Ramezani, A., Chung, S.-J., and Hutchinson, S., “A biomimetic robotic platform to study flight specializations of bats,” Sci. Robot. 2, eaal2505 (Feb. 2017).
  * [10] Ramezani, A., Shi, X., Chung, S.-J., and Hutchinson, S., “Lagrangian modeling and flight control of articulated-winged bat robot,” in [2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) ], 2867–2874, IEEE, Hamburg, Germany (Sept. 2015).
  * [11] Hoff, J., Ramezani, A., Chung, S.-J., and Hutchinson, S., “Synergistic Design of a Bio-Inspired Micro Aerial Vehicle with Articulated Wings,” in [Robotics: Science and Systems XII ], Robotics: Science and Systems Foundation (2016).
  * [12] Ramezani, A., Shi, X., Chung, S. J., and Hutchinson, S., “Nonlinear flight controller synthesis of a bat-inspired micro aerial vehicle,” in [AIAA Guidance, Navigation, and Control Conf. ], (2016).
  * [13] Hoff, J., Ramezani, A., Chung, S.-J., and Hutchinson, S., “Reducing Versatile Bat Wing Conformations to a 1-DoF Machine,” in [Biomimetic and Biohybrid Systems ], Mangan, M., Cutkosky, M., Mura, A., Verschure, P. F., Prescott, T., and Lepora, N., eds., Lecture Notes in Computer Science, 181–192, Springer International Publishing, Cham (2017).
  * [14] Ramezani, A., Ahmed, S. U., Hoff, J., Chung, S. J., and Hutchinson, S., “Describing robotic bat flight with stable periodic orbits,” in [Conf. on Biomimetic and Biohybrid Systems ], 394–405, Springer (2017).
  * [15] Syed, U. A., Ramezani, A., Chung, S. J., and Hutchinson, S., “From rousettus aegyptiacus (bat) landing to robotic landing: Regulation of cg-cp distance using a nonlinear closed-loop feedback,” in [Int. Conf. on Robotics and Automation (ICRA) ], 3560–3567, IEEE (2017).
  * [16] Hoff, J., Ramezani, A., Chung, S.-J., and Hutchinson, S., “Optimizing the structure and movement of a robotic bat with biological kinematic synergies,” The International Journal of Robotics Research 37, 1233–1252 (Sept. 2018).
  * [17] Hoff, J., Syed, U., Ramezani, A., and Hutchinson, S., “Trajectory planning for a bat-like flapping wing robot,” in [2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) ], 6800–6805, IEEE, Macau, China (Nov. 2019).
  * [18] Ramezani, A., “Towards biomimicry of a bat-style perching maneuver on structures: the manipulation of inertial dynamics,” in [2020 IEEE International Conference on Robotics and Automation (ICRA) ], 7015–7021, IEEE, Paris, France (2020).
  * [19] Sihite, E., Kelly, P., and Ramezani, A., “Computational Structure Design of a Bio-Inspired Armwing Mechanism,” IEEE Robot. Autom. Lett. 5, 5929–5936 (Oct. 2020).
  * [20] Sihite, E. and Ramezani, A., “Enforcing nonholonomic constraints in Aerobat, a roosting flapping wing model,” in [2020 59th IEEE Conference on Decision and Control (CDC) ], 5321–5327, IEEE, Jeju Island, Korea (South) (Dec. 2020).
  * [21] Trease, B. P., Moon, Y.-M., and Kota, S., “Design of large-displacement compliant joints,” Journal of Mechanical Design 127(4), 788–798 (2005).
  * [22] “Digital materials data sheet,” (2017).  [Online]. Available: https://www.stratasys.com/-/media/files/material-spec-sheets/mss_pj_digitalmaterialsdatasheet_0617a.pdf (accessed May, 2020).
  * [23] Shahzad, M., Kamran, A., Siddiqui, M. Z., and Farhan, M., “Mechanical characterization and fe modelling of a hyperelastic material,” Materials Research 18(5), 918–924 (2015).
  * [24] Hauser, H., Ijspeert, A. J., Füchslin, R. M., Pfeifer, R., and Maass, W., “The role of feedback in morphological computation with compliant bodies,” Biol Cybern 106, 595–613 (Nov. 2012).