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Single actuator wave-like robot (SAW): Design, modeling, and experiments



In this paper, we present a single actuator wave-like robot, a novel bioinspired robot which can move forward or backward by producing a continuously advancing wave. The robot has a unique minimalistic mechanical design and produces an advancing sine wave, with a large amplitude, using only a single motor but with no internal straight spine. Over horizontal surfaces, the robot does not slide relative to the surface and its direction of locomotion is determined by the direction of rotation of the motor. We developed a kinematic model of the robot that accounts for the two-dimensional mechanics of motion and yields the speed of the links relative to the motor. Based on the optimization of the kinematic model, and accounting for the mechanical constraints, we have designed and built multiple versions of the robot with different sizes and experimentally tested them (see movie). The experimental results were within a few percentages of the expectations. The larger version attained a top speed of 57 cm s(-1) over a horizontal surface and is capable of climbing vertically when placed between two walls. By optimizing the parameters, we succeeded in making the robot travel by 13% faster than its own wave speed.
Abstract— In this paper, we present a single actuator
wave-like robot (SAW), a novel robot which can move
forward or backward by producing a continuously
advancing wave. The robot has a unique minimalistic
mechanical design and produces an advancing sine wave,
with a large amplitude, using only a single motor but with
no internal straight spine. The direction of locomotion is
determined by the direction of rotation of the motor. A
kinematic model of the robot is developed that accounts
for the two-dimensional mechanics of motion and yields
the speed of the links relative to the motor. Based on the
optimization of the kinematic model, and accounting for
the mechanical constraints, we have designed and built
multiple versions of the robot with different sizes and
experimentally tested them (see movie). The experimental
results were within a few percentages of the expectations.
The larger version attained a top speed of 23 cm/s over a
horizontal surface and is capable of climbing vertically
when placed between two walls. By optimizing the
parameters, we succeeded in making the robot travel by
13% faster than its own wave speed.
In the last decades, multiple studies have analyzed the
locomotion of crawling robots inside tubes for maintenance
purposes and in biological vessels for medical applications.
In many of those applications, the robots must overcome
rough terrain characterized by anisotropic properties, high
flexibility, varying dimensions, and low friction coefficients
[1]-[4]. A key element in the design of small crawling robot
is a minimalist approach, i.e. small number of motors and
controllers, which allows for miniaturization. Two main
locomotion patterns have been investigated: worm-like
locomotion [5]-[26] and undulating locomotion which
resembles a continuously advancing wave [27]-[43]. Worm-
like robots advance by changing the distance between their
links [5]-[26]. There are two types of worm-like robots;
inchworm-like robots and earthworm-like robots. Inchworm-
like robots [5]-[16] are generally made of two cells
(sometimes three3 as in [15]) fitted with clamps to increase
or decrease the friction forces by changing the normal forces
or the coefficients of friction. Earthworm-like robots [17]-
[24] are made of a larger number of cells, often four or more.
Multiple mechanisms of locomotion were developed using
magnet coils [19], shape memory alloys [17], an external
electromagnetic field [20],[21] and inflatable cells [23].
The Authors are with the Mechanical Engineering Department of Ben
Gurion University P.O. Box 653 Be’er Sheva 8855630 Israel (e-mail:
This research was partially supported by the Helmsley Charitable Trust
through the Agricultural, Biological and Cognitive Robotics Initiative of
Ben-Gurion University of the Negev.
Using the inflatable cells approach, Glozman et al. [24]
applied one actuator and a single air/water source to drive an
inflatable worm made of multiple elastic cells inside the
intestines of a swine. Novel designs of inchworm-like and
earthworm-like robots actuated by a single motor were
developed by Zarrouk et al. [25],[26]. This minimalist design
allowed us to reduce the size, weight, energy consumption,
and to increase the reliability of the robot.
Fig. . The novel single actuator wave like robot (SAW). The robots have a
spine that constrains the links to move around it, producing an advancing
wave like motion (see movie .(
Wave-like locomotion was successfully produced by hyper
redundant snake robots [27]-[34] only (even though,
kinematically speaking a single actuator is required). The
first documented attempt to produce wave like locomotion
dates back to the 1920s by artist Pyotr (Petr) Miturich [41]
who suggested a design comprising an assembly of gears.
But nearly 30 years later the problem remained unsolved.
Taylor et al. (1951-1952) [36],[37][36], who investigated
the locomotion of wave-like and spiral-like locomotion in
low Reynolds environment, expressed his inability to
develop a mechanism that will allow to produce those
motions in order to experimentally validate his analysis.
More recently, some progress was reported by producing
cyclic motion with a small number of actuators which to a
certain extent resembles a wave but is actually a rigid straight
spine Error: Reference source not found-[41]. Other attempts
included producing a wave by vibrating a rod [42],[43], but
this method results in relatively small amplitudes whose size
is a function of the damping.
In this paper, we present the first single actuator wave-like
robot (SAW) which can produce a nearly perfect sinusoidal
advancing wave-like motion (Fig. ). In Section II, we
describe the kinematics of the wave locomotion. In Section
III, we present our novel design for the wave-like robot and
model its kinematics in Section IV. The kinematical model
Single Actuator Wave-Like Robot (SAW): Design, Modeling, and
David Zarrouk, Moshe Mann, Amotz Hess
was used to optimize the design of the robot. Finally,
experiments performed with the robots which we built are
presented in Section V.
In this section, we show that the projection of a rotating
helix forms an advancing sine wave.
A. Traveling wave
The simplest model of traveling wave is an advancing sine
wave, or harmonic wave. Its mathematical presentation is
( ) ( )
, siny x t A kx wt
= −
where x is the space coordinate, t is the time, y is the height
of the wave at point x and time t, and A is the amplitude. The
angular velocity w of the wave is related to the frequency by
and the wave length L of the traveling wave is related to the
wave number by
The travelling speed of the wave is thus
V f L k
= × =
B. Mathematical model of helix and its projection.
A helical curve with its axis in the x direction is described
parametrically by
( )
( )
x a
y A a
z A a
= ×
where L is the length of the pitch and A is the radius of the
helix and a is the independent paramter. The two
dimensional projection of the helix on the X-Y plane ( z = 0)
yields the following sine function:
( )
sin sin
x a
y A a A L
= ×
 
= =  ÷
 
A 3D helix whose axis is parallel to the x direction and its 2D
projection on the X-Y plane are presented in Fig. . Its
projection is a sine wave, as seen from Eq. )(
Fig. . A helix and its projection on the X-Y plane. The projection of the helix
is a sine wave, where the amplitude is the radius of the pitch .
C. Rotating helix and comparison to traveling wave.
When the helix rotates around its axis (the x axis) at a
constant angular frequency w (counterclockwise) the
parametric equations of the helix (Eq. ()) are multiplied by
the rotation matrix around the x axis:
( )
( )
( ) ( ) ( )
( ) ( ) ( )
( )
( )
( )
, 1 0 0 2
, 0 cos sin sin
, 0 sin cos cos
x a t
y a t wt wt A a
z a t wt wt A a
A a wt
A a wt
 
 
   
 
=  
   
 
   
 
 
 
 
= −
 
 
 
 
Inserting a = 2π/L*x into y demonstrates that the projection
of the rotating helix is an advancing sine wave given by:
In the previous section, we showed that the projection of a
rotating helix is an advancing sine wave. Our robot design,
which uses a single motor to produce an advancing wave,
follows the same concept. The robot is composed of four
main parts: the motor house, the motor, the helix, and the
series of links (Fig. ). The motor is attached to the motor
housing from one side and to the helix from the other side.
The links are attached to the motor house. As the motor
rotates the helix, the links cancel the rotation along the axis
of the helix and maintain the vertical motion. In this way, the
links act as a 2D projection of the helix of the robot.
The helix of the larger version is nearly 25 cm long and is
composed of two windings and a short extension to reduce its
diameter. Its external diameter is 5.2 cm and its radius is A =
2.1 cm. The links, presented in Fig. , are 7 cm wide 1.83 cm
high (r = 0.9 cm), and the distance between the joints of two
links is 1.2 cm (Llink = 1.2 cm). The smaller version is nearly
scaled down by a factor of nearly 2:1 and the smallest is
scaled down by a factor of 3:1. The helix and the links are
3D printed. The robot is fitted with a 6 Volt, 12 mm motor
with 300:1 gear ratio. Based on its catalog specifications, the
motors and gearbox produce a torque of 2.9 Kg-cm at 45
rpm. It is noted that in most of the experiments (except when
specified otherwise), we used a single ~4V lithium–ion
battery which is substantially lower than its nominal input (6
-9 Volts). The total weight of the larger robot including one
battery is 188 grams, whereas the smaller one weighed only
47 grams only.
Fig. . The different parts of the robot. The robot has a housing for the motor.
The helix is attached to the motor and rotates relative to the housing. The
links are attached to the housing and do not undergo roll rotation.
In this section, we model the kinematics of the links and
calculate their speed relative to the head of the robot (motor
housing) as a function of its frequency of locomotion f, the
wave length Lwave, the amplitude of the wave A, the length of
the link Llink, and its height r. If the links do not slide over the
surface, (as we experimentally found in section 5 - Fig. ), the
speed of the robot will be equal to the speed of the tips of the
links, along the axis direction. We define the advance ratio
(AR) as the speed of the robot Vrobot divided by the speed of
the travelling wave relative to the motor base Vwave:
wave wave
= =
where Vrobot is the speed of the robot, Lwave is the length of the
wave, and Lcycle is the net advance per cycle (one rotation of
the helix)
robot cycle
V f L
Fig. . The The geometry of the link. The two main parameters are the link
length Llink, the distance between two adjacent joint, r is the height of the link
and wtip is the width of the tip.
A. Kinematics of the links
As the wave advances, the links move both horizontally
and vertically. As the wave advances by Δx, the link will
rotate by Δα (see Fig. ).
( )
( )
( )
( )
( )
atan cos atan sin
x x
dA kx kA k x
 
∆ = =
 ÷
 
Due to the rotation, the tip of the link will move by a distance
( )
sinX r
∆ =
If the speed of the wave is Vwave, the time required by the
wave to advance by a distance of Δx is
t x V = ∆
Therefore the expected speed of the link is
Inserting Eqs. ()-() into Eq. () we obtain the speed of the tip
of the link
( )
( )
( )
sin tan sin
link wave
r a kA k x
− ∆
If we assume small angles
( )
( )
2 2
k x k x
a Ak x Ak x
≈ ∆
∆ ≈
And finally, by inserting Eq. () into Eq. (), one obtains the
speed of the tips of the links as a function of the height r,
amplitude A, wave length Lwave, and wave speed Vwave.
link wave wave
V rAk V rA V
 
=  ÷
 
Alternatively, the speed of the wave can be calculated as a
function of the actuation frequency:
( )
link wave
V rAk V r f
≈ =
Therefore the speed of the link is proportional to the ratio of
the amplitude divided by the wave length, to the height of the
links and to the actuation frequency. In theory, it would be
advantageous to increase A/Lwave and r to increase the speed.
However, increasing those values results in collision between
the tips of neighboring links. This collision is most likely to
occur when two links are symmetrically oriented towards
each-others such as links i-1 and i in Fig. case A. Assuming
zero width of the tips of the links, collision will occur when
/ 2
= ∆
 ÷
 
Inserting the value of Δα into from Eq. () into (), it is possible
to obtain the condition of collision as a function of the size of
the links and the wave parameters.
kA k
 
 
 ÷
   ÷
 ÷
 ÷  
= −  ÷
 ÷  ÷
 
 ÷  
 ÷ +
÷ ÷
   ÷
 ÷
 ÷
 
 
 
Fig. . The rotation of the links during the adavnce of the wave. “A” marks
the beignning of the touchdown of link i and retraction of link i-1. In “B”,
the wave has advanced by Δx and link i is at the lowest point of the wave.
“C”, which occurs after the wave advances by a further Δx, marks the end of
the touching of link “i” and the beginning of the engagement of i+1.
A. Kinematics of the links
We assume that the links slide along the advancing wave
(rotating helix) while the first link is attached to the motor
housing. The number of links is determined by the length of
the wave Ltot divided by the length of the links.
( )
L N y x dx
 
 
= +
 ÷
 ÷
 ÷
 
 
where N is the number of waves in the sine function (N = 2 in
our robot). Equation Chapter 1 Section 1To calculate the
positions of all the links of the robot, we sequentially solve
for the location of the endpoint of each link along the sine
wave. That is, we start with the location of the joint i of link
[xi yi] and solve for the x coordinate of the link’s endpoint
[xi+1 yi+1] by assuming that it is fastened to the sine wave
using the equation:
( ) ( )
2 2 2
1 1
sin( ) y
i i link
i i
x x A kx t L
+ +
+ − − =
where Llink is the length of each link. Solving Eq. () returns
the position of the end point xi+1 of link i. The endpoint of
link “i” serves as the start point of link “i+1”, and so on until
the last link’s location is solved for. The location of each
link’s start point and end point provides complete
information of the link’s orientation, and is used to calculate
the location of the links’ tip [x_tipi y_tipi]:
1 1
1 1
_ 0
_ 0
0 0 0 0 1
i i i i i i
i i i i i i
x tip x x x x x
y tip y y y y y r
+ +
+ +
− −
 
 
= + + − ×
 
 
 
The position of the links when the motor housing is fixed
was simulated using MATLAB (2013) program. Equations
() and () were solved at a rate of 500 times per cycle (results
and optimization are summarized in Fig. and in Ttable I).
The velocity is obtained by deriving the position as a
function of the time. In the simulation, we also accounted for
the width of the tip of the link, since in practice, the width
must be a few millimeters (in the simulation, we used wtip =
0.05 Lwave).
A two dimensional side projection of the simulated robot
is shown in Fig. . The robot consists of 25 rigid links
connected through revolute joints formed into a sine wave of
two spatial cycles. We focus here on the motion of link 5. As
link 5 approaches the lower bottom of the wave, it moves
slightly horizontally and rotates clockwise. Both of these
motions add up to move the bottom tip to the left, and
therefore the robot would move to the right.
Fig. . The simulation of the robot. The “motor housing” is rigidly fixed. As
the wave adavances from left to rightright to left, the lower tips of the links
which will be in contact with the surface move slightly towards the left and
rotate clockwise.
B. Expected robot advancement speed
The simulation allowed us to visually gain insights into
the motion of the links and optimize the design of the robot.
If no sliding occurs, the speed of the robot will be equal (but
to the opposite direction) to the horizontal speed of the links
contacting the surface. Therefore, the simulation calculates
the position of the different links at all times and detects
which of the links is the lowest, i.e. expected to be in contact
with the ground. Averaging the speed of the lowest tips yields
the expected speed of the robot.
In Fig. , we present the advance ratio as a function of the
amplitude for 3 different values of links heights (r/Lwave).
Since practically speaking, the tips of the links have a width
wtip, we determine the maximum value of the amplitude
which results in the collision marked with *. By assuming
that the width of the tips is 5% of the wave length, we found
that the maximum AR is limited to nearly 0.7 in all three
cases because of the collisions between the tips of
neighboring links. See our the Aappendix on how we
managed to overcome this limitation.
Fig. . The advance ratio as a function of the amplitude for three different
heights. The asterix (*) marks the limit for which two neighboring links will
collide with each others.
In Section IV, we calculated the speed of the links as a
function of the different robot parameters such as the length
of the wave, the distance between the links, and their width.
In this section, we will experimentally measure the speed of
our 3D printed robot and compare it to the results of the
simulation. The position of the robot is measured using a 12
cameras Optitrack setup with a frequency of 120 Hz. The
accuracy of the system is nearly 0.1mm. We designed a
special link for holding the reflective marker at the lower tip
of the link (Fig. ). The special link has a side attachment for
the marker in which the center of the marker is on the axis of
the contact line with the surface. Using this link, the marker
remained on the side of the surface and would not interfere
with the experiment. The speed is determined by deriving the
position as a function of the time.
Fig. . A special link was manufactured to hold the reflective marker. The
center of the reflective is along the axis of the tip of the link.
A. Speed of the links
In our first experiment, we determined the trajectory of the
lower tip of one of the links (using the special link) when the
robot motor house was rigidly fixed. The trajectory and the
orientation of the tip of 8 cycles are presented in Fig. . The
motion is very cyclic with very little difference between one
cycle to and another. During a cycle, the tip moves vertically
by nearly 4 cm. This result is slightly less than expected (2*A
= 4.2 cm) and probably due to slight spacing between the
links and the helix. The horizontal motion is nearly 2 cm.
However, the motion of the link from the onset of contact
until disconnecting from the surface is nearly 1 cm.
Fig. . The motion of the bottom tip of the link during 8 cycles when the
robot is not moving. The arrow show the direction of motion.
In the second experiment, the robot was free to advance
and the position of the links was measured using the
Optitrack setup. We performed the experiments over
plywood and over aluminum which has a lower COF with
the links (nearly 0.3 whereas the COF over plywood is nearly
0.4).The results of the trajectory and the speed along the x
axis are presented in Fig. (over aluminum surface). The
trajectory shows that the link touches the surfaces at a single
contact point. Therefore the link is not sliding over the
surface and its relative speed to the surface is zero. Sliding
didn’t occur also when the robot was run at higher speeds.
Fig. . (Top) The position of the lowest tip of a link during horizontal
locomotion over alumium surface. The single point contact at each cycle
proves that no slide between the links and the surface. (Bottom) The
horizontal speed of the links.
Table 1, summarizes the results of multiple experiments that
we performed by the smaller and bigger versions of our
robots. The data is the average of at least 12 cycles. The
results were compared to the simulations and found to be
within a few percentage of each-others. The larger and
smaller versions performed nearly similarly for two different
amplitude to wave length ratios. Following the predictions of
the simulation, we designed special links with large height
that allowed the robot to advance by 13% faster than the
speed of the wave (AR = 1.13). We note here that a short
survey that we made with multiple roboticists found that they
all believed it is impossible to advance faster than the speed
of the wave!
Table I. The advance ratio as a function of the slope.
Lwave A/Lwave r/Lwave Aver. AR STD ΔAR/Lcycle
[cm] [cm] [cm] Lcycle/Lwave AR
Large SAW
10.4 0.2 0.088 0.71 1.7% 2%
10 0.1 0.092 0.33 1.7% 5%
10.4 0.2 0.168 1.13 4.3% 2%
Small SAW
5 0.2 0.092 0.76 7.7% 8%
5 0.1 0.092 0.38 4.4% 8%
B. High speeds
We performed two more experiments to reach higher
speeds with the robot. In the first experiment, we used the
same set up, but we powered the robot with two Lithium-ion
batteries in series producing 8 Volts instead of a single
battery. The robot reached a speed of 10.4 cm/s. In the
second experiment, we attached three batteries in series (12
Volts) and used a 1:100 gear ratio (instead of 1:300). In this
configuration, the robot crawled at 23 cm/s. It is noted that
even at high speed no sliding was observed between the
robot and the surface.
C. Crawling over slopes and vertically between walls
We also the tested ability of the robot to climb by placing
the robot between two layers of polyurethane foam whose
COF with the links of the robot is nearly 0.4. The robot was
powered by two Litium ion battery (as it was not able to
move using a single one) and climbed at a speed of 8.2 cm/s.
The experiment is presented in Fig. . Note that in this
experiment, the two walls must be precisely distanced from
each other (up to a few millimeters of accuracy) in order to
achieve enough normal force for climbing, but without
overly pressing on the robot as it will stall.
Fig. . The robot climbing vertically between two walls. Using 8V input,
the robot reached a speed of 8.2 cm/s.
In this article, we developed a novel robot which generates
an advancing wave, that is nearly identical to a sine wave, by
rotating a helix that moves the links. The robot design is
simple, lightweight, cheap, and requires only a single motor
only to produce the wave. The direction of wave propagation
is determined by the sign of the voltage being applied to the
motor. We developed two prototypes:. tThe larger one with a
wave length of 10 cm thTand weighs only 188 gramsand a
1:2 smaller version weighing 47 grams. Both prototypes
proved to be highly reliable (considering that they are 3D
printed prototypes). During all of our experiments,
practically almost no maintenance was required.
We studied the kinematics of the links and developed a
simple model that explains how the motion is produced. The
model also predicts the approximated speed of the lower tips
of the links as a function of the wave length and amplitude
and size of the links. We also developed a simulation which
calculates the speed and visually presents the locomotion and
detects where collisions between the links will occur. The
simulation allowed us to visually comprehend the locomotion
mechanics and optimize the robot. We introduced the
advance ratio (AR) as the speed of the robot divided by the
speed of the wave. We found that in general, the AR is
smaller than 1, but by increasing the height of the links, the
advance ratio can be larger than 1 (A short survey between
roboticist showed us that they all believed that AR = 1 is the
maximum possible speed).
We measured the speed of the robot and the speed of the
lower tip of a link using an Optitrack system. By measuring
the speed of the lower tip of the link, we found that it
contacts the surface in at a single point, implying that not
sliding does not occurs. We performed multiple experiments
and found that they are all within a few percentages from the
expected speed by the simulation. By applying 12 Volts to
the motors, the robot moved at up to 23 cm/s and no sliding
was detected even in this case. The robot was also capable of
climbing vertically when finely placed between two surfaces
polyurethane foam at a speed of 8.2 cm/s.
Our future work will focus on analyzing the locomotion
of this type of robots over compliant and slippery surfaces.
A. Turning using steering wheels
We added steering wheels to the front of the robot as seen
in Fig. . The robot is now controlled using a two channel
joystick (extracted from an RC toy car - see movie). We
performed multiple experiment in crawling straight and
turning and captured the position using our Optitrack set up.
The results show that the robot can turn to either direction and
that the radius of turning was nearly 0.3 m.
Fig. . The robot with steering wheels. The direction of turning is
controlled by a second motor.
The results are presented in Fig. in which the name of the
robot is written (SAW). All the letters were completed in a
single run with no external intervention.
Fig. . The position of the robot with steering wheels. The robot wrote his
B. Increasing the height to travel faster than the speed of
the wave
To increase the speed of the robot beyond the speed of the
wave, we developed three sets of links with different tips
which do not collide with each-others (see Fig. ). The height
r was nearly 1.75 cm. Using those links, the robot achieved a
speed which is 13% larger than the wave speed.
Fig. . The specially designed links that do not collide with each others.
C. Miniaturization
To Tthe single motor design allows for further
miniaturization of the robot. Our smallest version (Fig. 15) is
12 cm long and 3 cm wide and weighs 30 grams including the
motor and battery. It was tested and shown to be crawling at
nearly 3cm/s (see movie). Further miniaturization of the robot
is possible and depends on more precise manufacturing.
Fig. . The smallest version of the robot. The length is nearly 12 cm and
the width is about 3cm.
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... Advanced robotic systems are often inspired by biological systems and organisms to achieve special movement capabilities. Examples are worm-like movements for crawling robots, insect-like movements for flying robots, and gecko-like movements for climbing robots [46][47][48] . The cutting edge of bioinspired robotics involves developing energy release mechanisms to generate jumping capacities [49] . ...
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Wild oat (Avena sterilis) is a very common annual plant species. Successful seed dispersion support its wide distribution in Africa, Asia and Europe. The seed dispersal units are made of two elongated stiff awns that are attached to a pointy compartment containing two seeds. The awns bend and twist with changes in humidity, pushing the seeds along and into the soil. The present work reveals the material structure of the awns, and models their functionality as two-link robotic arms. Based on nano-to-micro structure analyses the bending and twisting hygroscopic movements are explained. The coordinated movements of two sister awns attached to one dispersal unit were followed. Our work shows that sister awns intersect typically twice every wetting-drying cycle. Once the awns cross each other, epidermal silica hairs are suggested to lock subsequent movements, resulting in stress accumulation. Sudden release of the interlocked awns induces jumps of the dispersal unit and changes in its direction. Our findings propose a new role to silica hairs and suggesting a new facet of wild oat seed dispersion. Reversible jumping mechanism in multiple-awn seed dispersal units mays serve as a blueprint for reversibly jumping robotic systems. Statement of significance : The seed dispersal unit of wild oats carries two elongated stiff awns covered by unidirectional silica hairs. The awns bend and twist with changes in humidity, pushing the seed capsule along and into the ground. We studied structures constructing the movement mechanism and modeled the awn as a two-link robotic arm. We show that sister awns, attached to the same seed capsule, intersect twice every drying cycle. Once the awns cross each other, the epidermal silica hairs lock any subsequent movements, causing stress accumulation. Sudden release of the interlocked awns may cause the dispersal unit to jump and change its direction. Our findings suggest a new role to silica hairs and a new dispersal mechanism in multiple-awn seed dispersal units.
... STAR, which was developed by the same team, is a sprawl-tuned hexapod robot driven by three actuators: Two actuators work to drive the left and right legs, and the third actuator is used for the sprawl angle [24][25][26]. SAW is a robot that can be driven by a single actuator and can move forward by generating a wave-like motion [27,28]. SAW has a spine that constrains the links from moving around it, producing an advancing wave-like motion. ...
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The purpose of this paper is to design a lizard-inspired robot driven by a single actuator. Lizard-inspired robots in previous studies had the issue of slippage of their supporting legs. To overcome this issue, a lizard-inspired robot consisting of a four-bar linkage mechanism was designed. The purpose of this paper was achieved through three processes. The first process was kinematic analysis, where the turning angle and stride length of the robot were analyzed. The kinematic analysis results were verified via numerical simulations. The second process was the design and fabrication of the robot. For the robot’s design, both a shuffle-walking method utilizing a claw-shaped leg mechanism and a sliding-rod mechanism for equipping the actuator on the robot’s own coordinates were designed. The third process was experimental verification. The first experimental result was that the claw-shaped leg mechanism was capable of generating an 85.26 N difference in the static frictional force in the longitudinal direction. The other three experimental results were that the robot was capable of driving with 3.51%, 3.16%, and 3.53% error compared to the kinematic analyses, respectively.
... The two tendons contract and bend the body of the robot to create a peristaltic wave that moves the robot forward. Moreover, [18]- [20] developed a peristaltic robot using a cam-follower mechanism that they call single actuator wave-like robot. in [18], the mechanism uses a cylindrical cam; and in [19], [20], the mechanism uses a helix element as cam, and multiple links in parallel as followers. The helix determines the length of the peristaltic wave. ...
This paper presents an analytical description and experimental results for a reconfigurable field robot that can climb inside circular and rectangular pipes. The robot is fitted with two mechanisms that allow it to change its width and height and shift its center of mass (COM) to adapt itself to the size of the pipe. We start by describing the kinematic model of the robot as a function of its sprawl and four bar extension mechanism (FBEM). Next, we develop a force analysis based on the robot's geometry, its configuration, the position of its center of mass (COM), the diameter of the pipe, and the coefficient of friction (COF). We then develop strategies for driving, climbing and transitioning between the two modes. Although a high COF increases the robot's grip, it reduces its ability to reconfigure its shape, which it needs to transition between its climbing/driving modes. Based on this analysis, we designed a control algorithm comprised of actuation sequences to automatically drive the robot inside pipes, including the transition phases. The results show that the robot successfully executed its climbing tasks (see video).
Many marine creatures, gastropods, and earthworms generate continuous traveling waves in their bodies for locomotion within marine environments, complex surfaces, and inside narrow gaps. In this work, we study theoretically and experimentally the use of embedded pneumatic networks as a mechanism to mimic nature and generate bidirectional traveling waves in soft robots. We apply long-wave approximation to theoretically calculate the required distribution of pneumatic network and inlet pressure oscillations needed to create desired moving wave patterns. We then fabricate soft robots with internal pneumatic network geometry based on these analytical results. The experimental results agree well with our model and demonstrate the propagation of moving waves in soft robots, along with locomotion capabilities. The presented results allow fabricating soft robots capable of continuous moving waves using the common approach of embedded pneumatic networks and requiring only two input controls.
In this paper, a novel mobile mechanism based on Bennett mechanism is proposed, which can realize self-crossing locomotion. Unlike the most of the self-crossing mechanisms, the proposed mechanism can be assembled modularly, which has better environment adaptability. Firstly, on the basis of revealing mechanism of the self-crossing movement, configuration of the self-crossing mechanism is designed. The mechanism consists of n Bennett mechanisms connected in series by 2(n-1) 3R limbs that are symmetrically distributed on both sides of n Bennett mechanisms. Then, kinematic analysis of the mechanism is carried out based on finite and instantaneous screw theory, including mobility analysis and gait analysis. For the former, the number of degrees of freedom that the mechanism can achieve self-crossing locomotion is obtained, and for the latter, the trajectory of end point of the mechanism in the self-crossing movement is obtained. Finally, On the basis of theoretical analysis, simulation is conducted, and the results show that the proposed novel mechanism can realize self-crossing locomotion without interference, which verified the rationality of the mechanism. This paper provides a useful reference for the design and analysis of self-crossing mobile mechanism.
A detailed model for the locomotory mechanics used by millipedes is provided here through systematic experimentation on the animal and validation of observations through a biomimetic robotic platform. Millipedes possess a powerful gait that is necessary for generating large thrust force required for proficient burrowing. Millipedes implement a metachronal gait through movement of many legs that generates a traveling wave. This traveling wave is modulated by the animal to control the magnitude of thrust force in the direction of motion for burrowing, climbing, or walking. The quasi-static model presented for the millipede locomotion mechanism matches experimental observations on live millipedes and results obtained from a biomimetic robotic platform. The model addresses questions related to the unique morphology of millipedes with respect to their locomotory performance. A complete understanding of the physiology of millipedes and mechanisms that provide modulation of the traveling wave locomotion using a metachronal gait to increase their forward thrust is provided. Further, morphological features needed to optimize various locomotory and burrowing functions are discussed. Combined, these results open opportunity for development of biologically inspired locomotory methods for miniaturized robotic platforms traversing terrains and substrates that present large resistances.
This letter presents a minimally actuated Reconfigurable Continuous Track Robot (RCTR). The RCTR can change its geometry while advancing, thus enabling it to crawl and climb over different terrains and obstacles. The robot is fitted with a regular propulsion motor similar to a regular track and has a locking mechanism located at the front. The links have a unique design which allows them to be left loose to rotate between negative 20 to positive 45 degrees or be locked at zero or positive 20 degrees relative to each other as they reach the front of the robot. A release mechanism, located at the back, passively unlocks the links. As a result, all the links in the lower part are locked whereas the top links are unlocked. We first present the design of the robot and its mechanisms. Then, we model the kinematics and simulate the different shapes and obstacles that the robot can overcome. Finally, we present multiple experiments showing how this new robot can successfully navigate different obstacles (see video).
This paper analyzes the locomotion of a double screw-like robot composed of a right hand screw and a left hand screw attached via a rotating motor. Since the screws rotate in opposite directions, both screws produce propulsion in the same direction to advance. The advantage of this mechanism is that it can be used to crawl over deformable surfaces such as inside biological vessels and in granular media. We first develop a general analytical model of this double screw-like motion and describe its different modes of locomotion (raising-raising, raising-lowering, lowering-raising, lowering-lowering). We then use the model to determine the speed and forces acting on the robot as a function of the rotation speed, the screw geometry such as the diameter of the screw and its pitch, and the friction coefficient of the surface. The model is then used to evaluate the energy consumption of the locomotion and motor torques. The findings show that the surface forces acting on the two screws vary significantly if the coefficients of friction on each are different. The numerous new singular cases in which the screw forces can become infinite are discussed.
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In this work, we present a dynamic simulation of an earthworm-like robot moving in a pipe with radially symmetric Coulomb friction contact. Under these conditions, peristaltic locomotion is efficient if slip is minimized. We characterize ways to reduce slip-related losses in a constant-radius pipe. Using these principles, we can design controllers that can navigate pipes even with a narrowing in radius. We propose a stable heteroclinic channel controller that takes advantage of contact force feedback on each segment. In an example narrowing pipe, this controller loses 40% less energy to slip compared to the best-fit sine wave controller. The peristaltic locomotion with feedback also has greater speed and more consistent forward progress.
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We have developed several innovative designs for a new kind of robot that uses a continuous wave of peristalsis for locomotion, the same method that earthworms use, and report on the first completed prototypes. This form of locomotion is particularly effective in constrained spaces, and although the motion has been understood for some time, it has rarely been effectively or accurately implemented in a robotic platform. As an alternative to robots with long segments, we present a technique using a braided mesh exterior to produce smooth waves of motion along the body of a worm-like robot. We also present a new analytical model of this motion and compare predicted robot velocity to a 2D simulation and a working prototype. Because constant-velocity peristaltic waves form due to accelerating and decelerating segments, it has been often assumed that this motion requires strong anisotropic ground friction. However, our analysis shows that with smooth, constant velocity waves, the forces that cause accelerations within the body sum to zero. Instead, transition timing between aerial and ground phases plays a critical role in the amount of slippage, and the final robot speed. The concept is highly scalable, and we present methods of construction at two different scales.
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Motivated by the interest to develop an agile, high-efficiency robotic fish for underwater applications where safe environment for data-acquisition without disturbing the surrounding during exploration is of particular concern, this paper presents computational and experimental results of a biologically inspired mechanical undulating fin. The findings offer intuitive insights for optimizing the design of a fin-based robotic fish that offers several advantages including low underwater acoustic noise, dexterous maneuverability, and better propulsion efficiency at low speeds. Specifically, this paper begins with the design of a robotic fish developed for experimental investigation and for validating computational hydrodynamic models of an undulating fin. A relatively complete computational model describing the hydrodynamics of an undulating fin is given for analyzing the effect of propagating wave motions on the forces acting on the fin surface. The 3-D unsteady fluid flow around the undulating fin has been numerically solved using computational fluid dynamics method. These numerically simulated pressure and velocity distributions acting on the undulating fin, which provide a basis to compute the forces acting on the undulating fin, have been experimentally validated by comparing the computed thrust against data measured on a prototype flexible-fin mechanism.
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Unskillful operation and rough handling of conventional colonoscope, especially at the sigmoid colon, may lead to perforation or splitting the colon wall. Thus, it is crucial to develop autonomous or semi-autonomous colonoscopes that do not require physical force by the doctors for their motions. In this paper, we report the design and development of a colonoscopic robot system that has a locomotive function based on inchworm-like motion, with a hollow body and a steering system that consists of three pneumatic bellows of 7 mm diameter, each located 120 • apart from the others at the head part. The steering device can bend up to approximately 90 • . In order to evaluate the performance of the colonoscopic robot, in-vitro tests and in-vivo tests were carried out. The experimental results show the feasibility of the prototype colonoscopic robot being used for diagnosis and treatments in colon.
Worm-like robots for applications including maintenance of small pipes and medical procedures in biological vessels such as the intestines, urethra, and blood vessels, have been the focus of many studies in the last few decades. The robots must be small, reliable, energy efficient, and capable of carrying cargos such as cameras, biosensors, and drugs. In this study, worm locomotion along rigid and compliant terrain is analyzed, and a novel design of worm-like multicell robots actuated by a single motor is presented. The robots employ a screw-like axis for sequencing and coordination of the cells and clamps. This design allows for significant miniaturization and reduces complexity and cost. The design of the robots and analysis of their dynamics and power efficiency are described. Two earthworm and two inchworm prototypes were built to demonstrate their performance. The robots are capable of moving forward, backward, and vertically and consume low power, which allow them to climb for hundreds of meters using onboard batteries. [DOI: 10.1115/1.4005656]
In this article, we present the design, development, and characterization of a biomimetic robotic fish remotely controlled by an iDevice application (app) for use in informal science education. By leveraging robots, biomimicry, and iDevices, we seek to establish an engaging and unique experience for free-choice learners visiting aquariums, zoos, museums, and other public venues. The robotic fish incorporates a three-degree-of-freedom tail along with a combined pitch and buoyancy control system, allowing for high maneuverability in an underwater three-dimensional (3-D) space. The iDevice app implements three modes of control that offer a vividly colored, intuitive, and user-friendly theme to enhance the user experience when controlling the biomimetic robotic fish. In particular, the implemented modes vary in the degree of autonomy of the robotic fish, from fully autonomous to remotely controlled. A series of tests are conducted to assess the performance of the robotic fish and the interactive control modes. Finally, a usability study on elementary school students is performed to learn about students' perception of the platform and the various control modes.
This paper presents a proof-of-concept design of an inchworm-type piezoelectric actuator of large displacement and force (or power) for shape control and vibration control of adaptive truss structures. Applications for such actuators include smart or adaptive structural systems, auto and aerospace industries. The proposed inchworm-type actuator consists of three main components with frictional clamping mechanisms: two clamping or braking devices and one expanding device. The two frictional clamping devices provide alternating braking forces when the moving shaft, which is pushed by expanding device, walks inside the PZT tubular stack and emulates an inchworm, summing small steps to achieve large displacements. Since the development of a robust clamping mechanism is essential to realize the high force capability, a considerable design effort has been focused on optimizing the clamping device to increase the output force. CATIA is used as a platform to model the whole actuator and ANSYS is used to analyze and optimize the performance of the actuator. The proposed design avoids the tight tolerance of the tube diameters and reduces the clearance between clamps and the moving shaft with the adjustment device. The moving shaft of the actuator could also be replaced by one member of a truss structure for vibration suppression and position control purposes. In the proposed actuator the flexure clamps can also be easily replaced to outfit different dynamic characteristics. The complete design of the proposed actuator has been performed using the finite element analysis. The simulation result confirms that the output force of 160 N and incremental displacement in each step of 8.3 μm can be achieved using the proposed actuator. A prototype of actuator has been fabricated and static tests have been performed to validate the simulation results.
Large objects which propel themselves in air or water make use of inertia in the surrounding fluid. The propulsive organ pushes the fluid backwards, while the resistance of the body gives the fluid a forward momentum. The forward and backward momenta exactly balance, but the propulsive organ and the resistance can be thought about as acting separately. This conception cannot be transferred to problems of propulsion in microscopic bodies for which the stresses due to viscosity may be many thousands of times as great as those due to inertia. No case of self-propulsion in a viscous fluid due to purely viscous forces seems to have been discussed. The motion of a fluid near a sheet down which waves of lateral displacement are propagated is described. It is found that the sheet moves forwards at a rate 2pi 2b2/lambda 2 times the velocity of propagation of the waves. Here b is the amplitude and lambda the wave-length. This analysis seems to explain how a propulsive tail can move a body through a viscous fluid without relying on reaction due to inertia. The energy dissipation and stress in the tail are also calculated. The work is extended to explore the reaction between the tails of two neighbouring small organisms with propulsive tails. It is found that if the waves down neighbouring tails are in phase very much less energy is dissipated in the fluid between them than when the waves are in opposite phase. It is also found that when the phase of the wave in one tail lags behind that in the other there is a strong reaction, due to the viscous stress in the fluid between them, which tends to force the two wave trains into phase. It is in fact observed that the tails of spermatozoa wave in unison when they are close to one another and pointing the same way.
The action of the tail of a spermatozoon is discussed from the hydrodynamical point of view. The tail is assumed to be a flexible cylinder which is distorted by waves of lateral displacement propagated along its length. The resulting stress and motion in the surrounding fluid is analyzed mathematically. Waves propagated backwards along the tail give rise to a forward motion with velocity proportional to the square of the ratio of the amplitude of the waves to their length. The rate at which energy must be supplied to maintain the waves against the reaction of the surrounding fluid is calculated. Similar calculations for the case when waves of lateral displacement are propagated as spirals show that the body is propelled at twice the speed given it by waves of the same amplitude when the motion is confined to an axial plane. An externally applied torque is necessary to prevent the reaction of the fluid due to spiral waves from causing the cylinder to rotate. This is remarkable because the cylinder itself does not rotate. A working model of a spermatozoon was made in which spiral waves could travel down a thin rubber tube without rotating it. The torque just referred to was observed and was balanced by an eccentric weight. The performance of the model while swimming freely in glycerine was compared with the calculations. The calculated speed of the model was higher than was observed, but this discrepancy could be accounted for by the fact that the model has a body containing its motive power while the calculations refer to a disembodied tail.
The field of bio-mechanisms, which develops new machines that use motion and control of organisms as a model, is attracting attention. We examined the peristaltic crawling of an earthworm as a transport function in place of wheels or ambulation, and have developed a robot running inside a tube. In this robot, a joint corresponding to the earthworm's segment is driven by a DC motor. This paper presents the experimental result of the peristaltic crawling of an actual earthworm and the evaluation result of the transport mechanism of a prototype robot. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.