Modeling and Analysis on Exploration Rover with Screw Drive Mechanism
over Loose Soil
Kenji Nagaoka*, Takashi Kubota***The Graduate University for Advanced Studies (Sokendai), Japane-mail: nagaoka@nnl.isas.jaxa.jp**Institute of Space and Astronautical Science, JAXA, Japane-mail: kubota@isas.jaxa.jp

Abstract

rameters. Accordingly, it is practically difcult to dynamically control conventional wheeled or tracked robot onsoil to avoid a serious stuck. Further to this, essential
improvement of a locomotion mechanism should be also
conducted to cope with such difcult terrain.
Humans have been interested in ‘spirals’ due to its
geometric uniqueness in history [7]. Spiral structure has
been applied in versatile applications. As one typicalexample, an Archimedean screw mechanism has been
known as a screw-pump since early times [8]. So, the authors have proposed a mobile robot driven by such screw
mechanism for traveling on loose soil. The proposed system is expected to be robust to slipping and getting stuck
in loose soil because of the propulsive force in the axial direction of rotation. Combination of inclined screw bladesalso lead to movement in diverse direction. Furthermore,
its structural simplicity would be one of the advantages
as compared to a track. A screw driven vehicle like theproposed system, however, is not a new idea. In fact,
screw drive amphibians [9, 10] have utilized since morethan 170 years ago. And also, the screw locomotion wastried and tested when NASA developed the Lunar Roving Vehicles in Apollo missions [11]. To date, a small
number of experimental studies on the screw vehicle havebeen also reported [12, 13, 14]. But the soil-screw interaction is still unknown, and theoretical approaches toward
the understanding are extremely limited. Thus, the mathematical modeling of the soil-screw interaction becomesa new challenge to be elaborated because terramechanics
has mainly targeted just a wheel and a track. Likewise,
there have been several screw driven robots such as an invivo robot for laparoscopy [15, 16], an endoscope [17] ora spiral-type magnetic micro-machine [18]. In vivo robots
and swimming robots are typically moved by contact withviscoelastic biological tissue and incompressible viscousuid, respectively. Although they are equipped with thesimilar mechanism for locomotion, their targeted environments are quite different from terrain. Naturally, the respective models also differ on theoretical grounds.
From the foregoing considerations, this study focuses on the derivation of the novel soil-screw interaction

This paper describes the mathematical modeling andthe propulsion characteristics of a mobile robot driven by
an Archimedean screw units, called Screw Drive Rover.
In order to realize secure locomotion on loose soil, it isa serious issue for conventional wheeled or tracked locomotion to get stuck in the soil due to a slippage. On thispoint, the proposed rover is expected to be of robustness
to this issues. Furthermore, the rover can also travel invarious directions by using two screw units. However, theinteraction between such a screw unit and the soil is quite
complicated, and therefore, its detail remains undened.
This paper attempts to predict the tractive effort of Screw
Drive Rover on loose soil. To accomplish the theoreticalanalyses, the mathematical modeling is newly developed
based on soil-screw interactive mechanics. Finally, the validity of the model is demonstrated by simulations.

1 Introduction
Through recent space explorations, traveling or cruising technology on an extraterrestrial suraface has played asignicant role for mission successes. Recently the Mars
Exploration Rovers (MERs) demonstrated by NASA have
performed impressive achievements on Mars [1]. MERs
employ six wheels for locomotion on the martian terrain,
and until now these rovers have acquired scientic ndings for more than six years. In the meantime, a certain limitation of wheeled locomotion on loose soil has
came to light through the MER mission. Actually, MER
Spirit has been stuck in a sand trap [2], and then the rover
team eventually gave up on its extrication. In consideration of this, more theoretical discussions are required forlunar and planetary exploration rovers to assure robust locomotion on loose soil such as lunar regolith [3]. As one
promising approach for them, terramechanics investigating soil-vehicle interaction has received a lot of attention.
However, the interactive mechanics is fundamentally addressed based on semi-empirical static equations [4, 5, 6].
These equations are also comprised of some empirical pa-

i-SAIRAS 2010
August 29-September 1, 2010, Sapporo, Japan

162

Spur Gear

Dextral
Screw

Main
Body

Spur Gear

Bearing Folder

Hinge Leg

Body Frame

Rotaty Shaft
Hinge Leg

Coupling
Rotaty Shaft
Bearing Folder

Bearing Folder
DC Motor

Spur Gear

Spur Gear
Hinge Leg

Hinge Leg(a) Internal structure of main body and hinge legsSinistral Screw
Figure 1. Schematic of Screw Drive RoverCup Cover
Bearing
Hinge Leg

Cables-In Shaft

model. As the rst step, this paper addresses in particular
the interaction modeling based on conventional soil-wheel
model in terramechanics. In this paper, unlike the typicalwheel or track models, three-dimensional screw helicalmotion is newly considered. Characteristics of the developed model are elaborated by numerical simulations.

DC-Motor

Motor Folder
Sinistral Screw
Bearing
Cup CoverClyrindrical Shaft(for Screw Driving)
Connected Shaft
Hinge Leg(b) Cross-section diagram of screw drive unit

2 Proposition of Screw Drive Rover System

Figure 2. Mechanical structure of Screw Drive Rover

2.1 Conguration and Ideal Mobility

A novel rover equipped with Archimedean screw
drive units, called Screw Drive Rover, has proposed toachieve better locomotion on loose soil. Screw Drive
Rover is composed of a main body, hinge legs, and sinistral and dextral screw units winding N-times around eachcylinder, where the screw thickness is considered as a negligibly small value. In particular, this rover is able to drive
the hinge legs in synchronization to improve geometrically its stability. The authors have elaborated the mobility performance by applying the ideal kinematic model
so far [19]. Of particular note is that the modeled Screw
Drive Rover is capable of locomotion in diverse moving
directions by using just two driving units.

The results of the basic traveling tests on the test sand,which is quartz sand, are shown in Figure 3. From the results, it is conrmed that Screw Drive Rover can realize
multi-directional locomotion on sandy terrain by the twoscrew units. Furthermore, in some cases locomotion trajectories of the ideal model are different from ones of thetests. Hence, a more practical model is needed for pathfollowing or tracking control of Screw Drive Rover.

2.3

Challenge and Motivation

3

Modeling of Soil-Screw Interaction

3.1

Preliminary

On the basis of the previous traveling tests and theideal modeling, the development of a mathematical modelwith the soil mechanics would appear to be a next challenge. So, the interactive mechanics model between thesoil and the screw is derived based on terramechanics.
Then, the simulated tractive performances of Screw Drive
Rover are analytically discussed. The locomotion model
would particularly become a nonholonomic system, andtherefore, the modeling is of considerable signicance forthe achievement of desired movement.

2.2 Laboratory Tests

The authors have developed the Screw Drive Roverprototype to investigate briey its empirical mobility on
sand. Prior to the theoretical discussion, laboratory tests
have been conducted by using the prototype. Schematicof the prototype is shown in Figure 1. The screw units are
12.5mm in height and 55mm in outer diameter of screw’s
cylinder, and the screw slope angles are 16deg with N = 4.
The total system weights 6.4kg except for circuits and batteries. The overall conguration is approximately 200mm
in height, 300mm in width and 300mm in longitudinallength. Additionally, each screw unit can be driven independently by DC motors and thus diverse locomotive
directions are achieved as shown in Figure 2.

The motion states of Screw Drive Rover are preliminarily dened. Absolute coordinate system ΣO {X, Y, Z} is
set as illustrated in Figure 4. The modeling assumes a

163

Z
Y

ΣO

X
ω
p
y vy
v

z
ΣS
δ
vx
α x

Figure 4. Kinematics of sinistral screw unit
is dened as follows [5, 14].
⎧ pω/2π−vx⎪
if |pω/2π| ≥ |v x |⎪⎪⎪⎨ pω/2πsx = ⎪⎪⎪⎪⎩ pω/2π−vx
otherwisevx

Figure 3. Diverse mobility performance demonstrated
by Screw Drive Rover prototype on sandfamily of soil-screw moving together as one body. Further to this, the screw model technically depends on its
winding direction. But the denitions and formulas forthe modeling can be essentially regarded as common expressions. Therefore, unied expressions are describedfor each screw unit unless stated otherwise.

where ω is the screw angular velocity, v x is the velocity
component in x direction, 0 ≤ s x ≤ 1 under a driving stateand −1 ≤ s x ≤ 0 under a braking state.
Direction of locomotion is dened. Given the velocity
vector v in ΣS , the angle between v and the x axis can bedened as slip angle α [20]. By the velocity componentsv x and vy in ΣS , α is expressed as follows.
��(4)
α = tan−1 vy /v x

3.2 Screw GeometryFirst, the screw pitch and the slope angle are dened
as p and η, respectively. These values are constant andrepresented at the midpoint between the cylinder surface
and the screw blade edge. Here, p and η satisfy the following relation.
p = π (r + r1 ) tan η

On the contrary, v x and vy can be also written as a functionof s x and α.
vx =

(1)

where r1 is the screw cylinder radius, r2 is the screw
blade’s height and r is also dened as r = r1 + r2 . Here,the screw length b is dened as b = N · p.
The screw blade surface area, dA, at micro region dθfrom the screw winding angle θ, can be approximated asfollows.
dA(θ) = π (r2 − r12 ) · dθ(3)pω (1 − s x )
,
2π

vy =

pω (1 − s x )
tan α
2π

(5)

3.4 Formulations of Contact Stress3.4.1 Normal Stress

One of the signicant subjects in the study of terramechanics is the relationship between normal stress σ andsinkage h. The relational angle expression is rst given as
follows [5, 23].

(2)

The locomotion is basically governed by forces on dA.

θm = (c1 + c2 s x ) θ f

3.3 Kinematic Denitions(6)

where c1 and c2 are coefcients depending on the soilscrew interaction. Technically, while the slip direction in
Equation (6) does not necessarily correspond to s x , theauthors employ this relation like the conventional study
on wheels [21].
Next, the normal stress distribution of the soil beneaththe screw unit can be calculated as follows [5].
⎧n⎪if θm ≤ θ ≤ θ f⎪⎨ σm Θ1
σ(θ) = ⎪(7)⎪⎩ σm Θnotherwise

The screw xed coordinates ΣS {x, y, z} is rst set tobe the right-handed coordinate system with the x and yaxis in the longitudinal and vertical directions of the screw
unit. Figure 4 shows the kinematic model of the screw
unit. ΣS is dened as the rotating frame to ΣO , which rotates around Z axis by δ. Here, robotic locomotion on soil
is fundamentally accompanied with slip because of soil
compaction and failure. Assuming the rover’s attitude rotations around x and y axes are zero, the slip in x axis, s x ,

2

164

r R
θr

b

2r1

θ’r
θ=0

ω
θf

θf [deg]

2r

τ
h
θ

σ

Figure 5. Interactive mechanics of soil and screw unit

3.4.2

Shear Stresswhere τmax is shear strength, φ is soil internal friction angle, c is soil cohesion, j is soil displacement and K is shear
deformation modulus.

where θ is the screw angle (θr� ≤ θ ≤ θ f ), θr� (≤ 0) is the effective exit angle, θ f (≥ 0) is the entry angle, θm is the specic wheel angle at which the maximized normal stressoccurs, b is the screw’s longitudinal length, n is sinkage
exponent, and kc and kφ are pressure-sinkage moduli regarding cohesion and internal friction, respectively. Let R
be the elliptic distance as illustrated in Figure 5, and will
be dened later on. Also, θ f is geometrically derived by
the following equation.

3.4.3

Shear Displacement of SoilIn this paper, unlike the traditional approaches ofwheels, it is considered the soil between the screw blades
move as one body with the blades. That is, the soil
shear stress occurs along the outermost radius of the screw
blade. Consequently, the three-dimensional expression of
the screw’s helical trajectory is needed for giving the soil
thrust of the screw units by τ component. So this paper
provides the screw motion trajectory in ΣO , T (X, Y, Z),
by the following expression.

(11)

In �the� conventional
study in terramechanics, the con� �
dition ��θr �� ≤ ��θ f �� is basically premised for the expressionof σ beneath a rigid wheel. Figure 6 depicts the relationship between θ f and h/r. This provides h/r ≈ 0.29 atθ = 45deg.
� ��On� the other hand, in the case of the screw
unit, ��θ f �� ≤ ��θr �� has been observed through the travelingtests by the authors. This implies the reaction force fromdischarging soil is too�� ��small,� �and therefore, the stress dis�θ f � ≤ ��θr �� is obtained. So, this paper
tribution �satisfying� � �
assumes ��θ f �� ≤ ���θr ��� by �meansof a transformation of θr to�
θr� . θr� achieving ��θr� �� ≤ ��θ f �� is given as follows.
θr� = −c3 θ f

2

The shear stress of loose soil, τ, is generally formulated as follows [22].
��(13)
τ(θ) = τmax · 1 − exp− j/K(14)
τmax (θ) = c + σ tan φcos θ − cos θ f
(8)
�
�
� �
�
θ − θrθ f − θm − cos θ f (9)Θ2 (θ) = cos θ f −θm − θr���(10)
σm = kc /b + kφ Rn=

θ f = cos−1 (1 − h/r)

0.5
1
1.5
Sinkage / Radius, h /r

Figure 6. Relation between θ f and h/r

and also,Θ1 (θ)

180
150
120
90
60
30
0
0

and also,⎛⎞T⎜⎜⎜ r cos θ sin δ + VX t + X0 ⎟⎟⎟⎜⎟T = ⎜⎜⎜⎜ r cos θ cos δ + VY t + Y0 ⎟⎟⎟⎟⎝⎠
r sin θ + Z0⎧⎪⎪
⎨ VX = v x cos δ + vy sin δ⎪⎪⎩ VY = −v x sin δ + vy cos δ

(15)

(16)

where (∗)T denotes matrix transposition.
Then, the trajectory of the soil shearing is dened byangle γ (= π/2 − η) as illustrated in Figure 7. This trajectory PE (XE , YE , ZE ) basically traces an ellipse. In thescrew xed elliptic coordinates ΣE {XE , YE , ZE }, PE can bederived by β or θ (= β − 3π/2).

(12)where c3 (≤ 1) is a positive angle coefcient.
The screw unit provides a elliptic cross section for discussing the normal and the shear stresses with angle θ as
illustrated in Figure 5. In wheels, while the soil is shearedin elliptic trajectory when a wheeled vehicle steers, thecommon formula of the normal stress is applicable [20].
Hence, this paper also employs the unied normal stress
distribution Equation (7).

⎞T ⎛ −r⎞T⎛ r⎜⎜⎜ cos γ cos β ⎟⎟⎟⎜⎜⎜ cos γ sin θ ⎟⎟⎟⎟⎟⎜⎜PE = ⎜⎜⎜⎜ r sin β ⎟⎟⎟⎟ = ⎜⎜⎜⎜ r cos θ ⎟⎟⎟⎟
⎠
⎠
⎝
⎝
0
0

(17)

The tangential equation at a certain point (xa , −ya ) on

165

Effective Shearing Distance, ds

r1(a) Trajectories of screw blade and soil displacementrηr + r12

π/2 - ηElliptic Equation
YE X 2E + Y E2 cos2γ = r 2

γ
-r
cosγ

XE

r
β

r
cosγ

YE

π (r + r1) tanη
2

XE
ξ

2r

ds / π (r+r1)

PE is also represented as follows.

L

d
L
dt

(20)

(24)

15

30

45
60
η [deg]75

90d(T + PO )dt⎛⎞Tp(1−s x )⎜⎜⎜⎟⎟⎟− r cos θ sin γ
2π
⎜
⎟⎟⎟
x)
= ⎜⎜⎜⎜⎜ p(1−s(sin⎟⎟⎟ · ω
tan
α
−
r
θ
+
cos
θ
cos
γ)
⎝ 2π
⎠
r
r cos θ + cos γ sin θ��
Lv jx Lv jy Lv jz · ω
=
(25)
=

L

3.4.4

PO

1

where δ and δ are assumed to be zero.
Therefore, Equation (22) can be nally expressed asfollows.
�� θf �
j(θ) =
v j · dt =L2v jx + L2v jy + L2v jz · dθ (26)

(22)

(23)

T + PO⎛⎞T⎜⎜⎜ −r sin θ · sin (δ + γ) ⎟⎟⎟⎜⎟= ⎜⎜⎜⎜ −r sin θ · cos (δ + γ) ⎟⎟⎟⎟⎝⎠
−r sec γ · cos θstheir coordinates ΣE → ΣO . In light of Equation (5), thetime derivative of L is given as follows.

(19)

L =

f ≥0

Figure 8. Effective distance of soil shearing

Furthermore, the ellipse radius R can be formulated as afunction of θ by�R(θ) = r cos2 θ + sin2 θ · sec2 γ(21)
As a result, j is dened as follows.
�
v j · dtj(θ) =

fs ≤ 02(b) Parametric analysis of d s depending on η

Accordingly, the inclination angle of the tangent, ξ, canbe written as follows.
ξ = tan−1 (− cos γ · cot β) = tan−1 (cos γ · tan θ)

3

0
0

(18)

where xa and ya are positive values, and the sinkage is assumed to be less than r. Substituting Equation (17) into
Equation (18), the above equation can be eventually simplied as follows.
cos γ
r cos γya = −· xa +tan β
sin β

Screw Cylinder

4

Figure 7. Elliptic trajectory of soil shearingxaya· XE + 2 · YE = 1
2
2
r sec γr

π (r + r1) cosη2(a) Illustration of effective shearing distance-r(b) Denition of soil shearing ellipse

and also,

Screw Bladepθ

Stationary State of Dynamic Sinkage

On the basis of the study by Yamakawa et al. [24], thewheel’s dynamic sinkage reaches a stationary state when
the wheel drives with a constant slip. The stationary sinkage is ultimately proportional to the wheel slip, and the
proportionality factor depends on both the wheel and thesoil. So, this study assumes the following relationship ina similar way for subsequent simulation analyses.

where L is the trajectory of the displaced soil in ΣO and v j
is the relative soil displacement velocity along L. Moreover, PO gives a transformation from PE , transformingh = h0 + c4 s x

166

(27)

−0.5
−1
0

−sinθ
15

30

45 60
θ [deg]

−sinξ
75

90

1

cosξ

0.5 η = 30deg
0

−0.5
−1
0

−sinθ
15

30

cosθ
−sinξ
45 60
θ [deg]75

Angle Components
for Tractive Effort

0.5 η = 15deg cosθ
cosξ
0Angle Components
for Tractive Effort

Angle Components
for Tractive Effort

1

1
0.5 η = 45deg
0

−0.5

90

−1
0

−sinθ
15

30

cosξ
cosθ
−sinξ
45 60
θ [deg]75

90

Figure 9. Angle components for tractive effort of stresses on circular and elliptic surfaces along angles
Likewise, the tractive effort in y direction is computed by�Fy =sgn (ω) F sin η(33)

where h0 is static sinkage before driving, c4 is a positivecoefcient. This enables us to simulate the relativity ofthe slip and the sinkage.

3.4.5 Soil Shearing Distance

where this paper assumes the body rotation δ is ignored asa primary analysis, giving δ = δ = 0.

The effective distance of the soil shearing, d s , is geometrically constrained by η and p as illustrated in Figure8(a). To evaluate the distance, the effective factor f s ishere given as follows.
p π (r + r1 ) (tan η + cot η)
fs =
−
r1
2r1

4.2

Advantage of Stresses on Elliptic Surface

5

Simulation Analysis of Tractive Effort

5.1

Parameter Conditions

Tractive components of the normal and the shear
stresses acting on an elliptic surface is generally different from the ones on a circular surface. In the developed model, τ acts as τ cos ξ and σ as −σ sin ξ for thetractive effort in x direction. On the other hand, τ actsas τ cos θ and σ as −σ sin θ for a wheel. With consideration of Equation (20), the active angle component of
the each stress for the tractive effort is shown in Figure
9. These results indicate the elliptic surface has an advantage over the circular one with smaller η. Furthermore, Figure 10 plots the ideal integrated angle compo�θnents for the tractive efforts, 0 (tan φ cos θ − sin θ) dθ and�ξ(tan φ cos ξ − sin ξ) dξ. Here, the integrating compo0
nents assume the available maximum shear stress of cohesionless soil in Equation (13), which is τ = σ tan φ. The
simulated plots indicate the elliptic surface works better
than the circular surface. It is also conrmed that the ratioh/r becomes a critical factor for the genesis of the tractive
effort.

(28)

Thus, d s is maximized with the positive f s . Contrary
to this, when f s is negative, d s is conned to the interscrew area. The positive f s obviously appears at 45deg≤η ≤90deg. Consequently, d s can be introduced as follows.
⎧ π(r+r1 ) tan η⎪
if f s ≥ 0⎪⎪
2 sin η⎪⎨(29)
ds = ⎪⎪⎪⎪⎩ π(r+r1 ) tan ηotherwise
2 cos ηFigure 8(b) depicts the parametric characteristics of d s
pertaining to η. According to this, it can be conrmed
d s is strongly governed by η.

4 Synthetic Locomotion Model
4.1 Integrated Tractive Efforts

In accordance with the interaction model of the soil
and the screw unit, the next is the introduction of the tractive efforts of Screw Drive Rover. The integrated tractive
effort in x direction of Screw Drive Rover is dened as F x
and is calculated as follows.
�sgn (ω) F cos η
(30)
Fx =
��
(τ cos ξ − σ sin ξ) dAdθ
F =
(31)

Through the simulations, the tractive effort F x is calculated when Screw Driver Rover travels in a straight line.
This provides δ = 0 and α = 0 as kinematic constraints.
By reference to the experiments by Dugoff et al. [14], s x
is similarly set to be a variable parameter. With respect tothe kinematic and geometric conditions, the nominal parameters are set: N = 4, η = 5 ∼ 30deg, r1 = 0.035m,
r2 = 0.015m, h = 0.01 ∼ 0.04m (h0 = 0.01m), ω =± π2 rad/s. Likewise, according to the experimental data targeting the sampled lunar soil [25] and the previous works[21], each soil parameter is set: K = 0.018m, c = 0.17kPa,
φ = 35deg, c1 = 0.4, c2 = 0.15, c3 = 0.2 ∼ 0.8,

�
where denotes the summation of the screw units. Let
the integral region be determined based on d s . Here, because the tractive effort is evaluated by whole integration,
Equation (31) can be modied as follows.
� θf(τ cos ξ − σ sin ξ) dθ
F = b · R sin η
(32)
θr�

167

Elliptic Surface

0.2
0

15

30

45 60
θ [deg]

75

90

−0.2

0.2

−0.4
0

15

30

45

θ [deg]

60

75

90

0.2
tanφ = 0.5
tanφ = 0.6
tanφ = 0.7
tanφ = 0.8
tanφ = 0.9

15

30

50

0
0

Tractive Effort, Fx [N]Integrated Angle Component
for Tractive Effort

0.4

−0.4
0

100

45

θ [deg]

60

75

0.2

0.4

0.6

Slip, sx

0.8

1

350
300
250
200
150

c = 0.23c3 = 0.5
c3 = 0.8

100
50

0
0

0.2

0.4

0.6

Slip, s0.81(b) With varying c3 , η = 16deg and c4 = 0.03

0.6

−0.2

η = 30 [deg]x(b) Circular surface0η = 16 [deg]150

Tractive Effort, Fx [N]Integrated Angle Component
for Tractive Effort

0.4

−0.2

η = 5 [deg](a) With varying η, c3 = 0.2 and c4 = 0.03

0.6

tanφ = 0.5
tanφ = 0.6
tanφ = 0.7
tanφ = 0.8
tanφ = 0.9

250
200

−0.4

(a) Comparative distributions

0

300

x

0.4

Circular Surface

350

Tractive Effort, F [N]Integrated
Angle Component
for Tractive Effort

0.6
0.4
0.2
0
−0.2
−0.4
0.5
0.6
0.7
tanφ
0.8
0.9 0

180
150
120
90

c4 = 0.03
c4 = 0.02
c4 = 0.01

60
30
0
0

0.2

0.4

0.6

Slip, sx

0.81(c) With varying c4 , η = 16deg and c3 = 0.2

90Figure 11. Tractive effort and slip of Screw Drive Rovermodel with varying parameters(c) Ellipse surface

Figure 10. Integrated angle components for tractive
effort of normal and shear stresses

crease of the exit angle θr� introduces larger F x . Although
this indicates an increase of contact surface is signicant,c3 is unlikely to have a signicant impact on F x , comparedto η. Further to these, Figure 11(c) shows the tendency
that the sinkage h exerts an effect on F x . With respect toh, F x possesses a maximum value. Better understandingof c4 is needed in the future work.
On the whole, the ratio of the sinkage and the radiush/r becomes one key factor in the light of Figure 10. The
increase of the contact surface is expected to generate alarger F x . However, the increase of h should be avoided
even if the contact surface enlarges. An appropriate control of h/r is the most important technique for the enhancement of mobility performance of Screw Drive Roveron loose soil. So that Screw Drive Rover always generates
positive tractive efforts, the design of η also becomes another important factor.

c4 = 0.01 ∼ 0.03, n = 1.0, kc = 1379N/mn+1 andkφ = 814.4kN/mn+2 .

5.2 Result and Discussion

Figure 11 plots the simulation results performed by
the proposed model. These results show the predictedtractive effort F x with the slip s x . According to these, it
is conrmed F x increases with an increase in s x in mostsituations. This typical tendency was observed in the pastexperiments [12, 14], and therefore, this conrms the validity of the model. Next, Figure 11(a) indicates the slope
angle η has little effect on F x until s x = 0.5. In contrast, an
increase in η results in a pronounced increase in F x unders x � 0.5. From this, large sinkage induces a decrease ofF x . Moreover, Figure 11(b) shows the tendency that an in-168

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This paper presents the novel robot system using
the Archimedean screw mechanism and its mathematicalmodel for traveling on loose soil. The proposed model isdeveloped based on the constracted terramechanics modelwith the screw geometry. Additionally, the soil shearing
ellipse is newly employed, and then the shearing trajectory is represented three-dimensionally. In this paper the
dependence of the model parameters is elaborated throughthe simulation analyses. Consequently, the advantage ofthe locomotion on loose soil by the screw units can be indicated. In particular, it is conrmed the screw units is aneffective structure to avoid getting stuck.
As for future works, experimental validation is required to evaluate and grasp the detailed interaction of thesoil and the screw unit. Further to this, the feedback fromexperiments to the model should be accomplished in orderfor enhancements of the model’s feasibility.

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