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22
Feasible Human-Spine Motion Simulators
Based on Parallel Manipulators
Si-Jun Zhu
1,2
, Zhen Huang
2
and Ming-Yang Zhao
1
1
Shenyang Institute of Automation (CMS)
2
Yanshan University
P.R. China
1. Introduction
In biological kinematics, motion of a spine is realized by a number of functional spinal units
(FSU), as shown in Fig.1 (spineuniverse.com). Each FSU consists of two adjacent vertebras
and physiological organization joining FSUs end-to-end (Hou, 2005). Owe to the spine,
vertebrates have more flexible torsos than others. To understand, simulate and utilize the
motion of vertebrate’s torso, international researchers have made many bio-vertebrate
robots such as robotic dog (bostondynamics.com), fish (robotic-fish.net), snake (Hirose;
nasa.gov; ri.cmu.edu; snakerobots.com), rabbit (jsk.t.u-tokyo.ac.jp), lizard (birg.epfl.ch) and
humanoid robot (kawada.co.jp; sony.net; world.honda.com; Giuseppe et al., 2003).


Fig. 1. A human-spine and FSU physiological organization
Torsos of some bio-vertebrate robots adopt torsos without bio-spine structure. As the most
advanced quadruped robot on Earth, BigDog (bostondynamics.com) adopted rigid torso

which result in the failure to realize the motion between shoulder and waist.
Parallel Manipulators, Towards New Applications

498
To improve flexibility, some bio-vertebrate robots adopt bio-spine torso, which means a
number of functional kinematic units (FKU, working as FSU) joined end-to-end through
joining structure. Similar with the spine for vertebrates, the bio-spine torso enable
maneuverability of bio-vertebrate robots. High maneuverability qualifies robotic fishes for
the oceanographical observation, the leak detection on pipelines, the search for mines and
the underwater archaeological exploration (robotic-fish.net). It also makes robotic snake be
competent for search-and-rescue mission (ri.cmu.edu), exploring and building in space
(nasa.gov) and moving both in water and on ground (Hirose).
Humanoid robots, as an special class of bio-vertebrate robots, have much wider applications
than others. Researchers believe humanoid robots may be adopted in entertainment,
cooperative works, maintenance and security task (Kazuo, 2003). Torsos of these robots are
carried out in different ways (kawada.co.jp; sony.net; world.honda.com; Giuseppe, Hun-ok
et al., 2003). ASIMO will realize 3-DoF for head and 1 for torso in next generation
(world.honda.com); SDR-4X II realized 4-DoF for neck and 2 for torso (body) (sony.net);
HRP-2 realized 2-DoF for head and 1 for torso (body) (kawada.co.jp); WABIAN-RV realized
4-DoF for neck and 3 for torso (Trunk) (Giuseppe, Hun-ok et al., 2003). From a medical point
of view, vertebras of human being are joined by intervertebral disc, ligaments and etc.
Translation for one end of a spine to another along the axis of spine is mainly realized by
bending, stretching and compressing ligaments and intervertebral discs. The range of such a
translation is so small that can be ignored. Therefore, one end of spine for human has 3
rotational and 2 independent translational DoFs (3R2T) relative to another instead of
theoretical 6 DoFs.
To the best of our knowledge, most existing humanoid robots accomplish motion of torso
through a serial mechanism. For a serial manipulator, the motor closed to the base has to
bear the mass of the motors closed to the manipulating end. Consequently, the link closed to
the base is much stronger than that closed to the manipulating end, which exhausts extra

energy and slows down the reaction. Different with a serial manipulator, a parallel
manipulator may assembled all motors on the base. Such a base-actuator structure will
lighten links and consequently improve working speed. For example, DELTA, a famous
successful parallel manipulator, “the use of base-mounted actuators and low-mass links allows the
mobile platform to achieve accelerations of up to 50 G in experimental environments and 12 G in
industrial applications” (parallemic.org). Moreover, kinematic performance of a spine for
vertebrate is closed to isotropy. However, a parallel manipulator does not necessarily have
isotropic kinematical performance as a serial manipulator. To achieve the kinematical
performance closed to isotropy, a parallel manipulator should be fully-symmetrical (FSPM)
(Mohamed, 1984), which means identical limbs, symmetrical assembly condition and
actuating mode.
To simulating the motion of a human spine, the manipulator should satisfy not only on
mobility property, reachable workspace and isotropic kinematical performance, but static
and dynamic performance. A spine of human usually can work under two different modes:
active mode and passive mode. Under active mode, muscles and ligaments control the
motion of the spine following the person’s will. Under passive mode, the spine passively
moves under the outside load. To satisfy both modes, the manipulators had better to have
less prismatic or cylindrical pairs considering that passive translation may result in extra
resistance caused by non-coaxial and low working speed especially for ball screw, which
will lead poor mechanics performance.
Feasible Human-Spine Motion Simulators Based on Parallel Manipulators

499
Considering the requirement mentioned above, a 3R2T 5-DoF base-actuator FSPM without
prismatic or cylindrical pairs is necessary for an simple and efficient spine motion simulator.
In the currently study, three such manipulators, 5-RRR
(RR), 5-(RRR)RR and 5-(RRR)(RR)
had been selected as the spine motion simulators. Respective kinematics properties are also
illustrated and compared with each other. On this basis, a 5-RRR
(RR) prototype is designed

and manufactured as the human spine motion simulator prototype. Motion capacity
between the prototype and different parts of human spine are compared. In the rear part of
the literature, future work for further improve the simulation capacity of the prototype is
planned.
2. Manipulator enumeration
Type synthesis of 3R2T FSPM had been a difficulty (Merlet, 2000) and hot topic until dozens
of them are proposed (Jin et al., 2001; Fang & Tsai, 2002; Huang & Li, 2002; Kong & Gosselin,
2002; Giuseppe, Lim et al., 2003; Li et al., 2004). Comparing with the degree of concern for
them in type synthesis, their application seems to be an inactive area.


(a) 5-RRR(RR) (b) 5-(RRR)RR (c) 5-(RRR)(RR)
Fig. 2. Three FSPMs for spine-motion simulator
Among near twenty theoretical types of 3R2T FSPMs currently, there are only three
manipulators without passive prismatic and cylindrical pairs, including 5-RRR
(RR), 5-
(RRR)RR
, 5-(RRR)(RR) as shown in Fig.2, where “AB” denotes axes of pairs A and B are
parallel, “(AB)” denotes axes of pairs A and B intersect at a common point.
2.1 5-RRR(RR)

(a) (b)
Fig. 3. 5-RRR(RR)
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500
For a 5-RRR
(RR) parallel manipulator shown in Fig. 3, the movable and base platforms are
connected by five identical limbs each with five revolute joints. Axes of three joints adjacent
to the base platform are perpendicular to the base; the other two intersect at point O

2
. The
line passing through the origin O
1
and O
2
is perpendicular to the base platform. Let the x-
axis be normal to axis of the first joint and z-axis point from O
1
to O
2
. In such a coordinate
frame, the reciprocal screw (Ball, 1900; Hunt, 1978) of limb screw system is $
r1
= [0,0,1; 0,0,0],
whose axis is normal to the base, as shown in Fig. 3(b). The reciprocal screws of five limbs
are the same. So the five constraints exerting on the movable platform form a common
wrench with zero-pitch which constrains the translational freedom along the z-axis. So the
movable platform has three rotational and two translational freedoms in a plane parallel to
the base platform. As all actuators are locked, the screw system changes to be
$
2
= [S
2
; S
02
] = [0,0,1; p
2
,q
2

,0]
$
3
= [S
3
; S
03
] = [0,0,1; p
3
,q
3
,0]
$
4
= [S
4
; S
04
] = [l
4
,m
4
,n
4
; p
4
,q
4
,0]
$

5
= [S
5
; S
05
] = [l
5
,m
5
,n
5
; p
5
,q
5
,0] (1)
According to the screw theory (Ball, 1900; Hunt, 1978), it can be found that $
r1
and $
r2
are the
reciprocal screws for the screw system expressed in Eq.(1) by inspection,

shown in Fig. 3(b).
The axis of $
r2
is the intersecting line of two planes P
R2R3
and P
R4R5

. P
RiRj
denotes the plane
determined by the axes of kinematic pairs R
i
and R
j
. The equation system for the axis of $
r2

is
N
1
· [x-x
R2
, y-y
R2
, z-z
R2
] = 0
N
2
· [x-x
o2
, y-y
o2
, z-z
o2
] = 0 (2)
where N

1
and N
2
denote the normal vectors of the plane P
R2R3
(N
1
· S
2
= N
1
· S
3
= 0) and plane
P
R4R5
(N
2
· S
4
= N
2
· S
5
= 0), respectively. [x
o2
, y
o2
, z
o2

] and [x
R2
, y
R2
, z
R2
] are the coordinates of
O
2
and the center point of the 2
nd
kinematic pair adjacent to the base, respectively.
In the general configuration, five $
r2
of five limbs are linear independent and every $
r2
is
linear independent with the common constraint $
r1
. So there are six linear independent
constraints exerting on the movable platform when the five actuators are locked. Therefore
the selection of the base actuators is feasible and the manipulator is fully-symmetrical.
However, the manipulator will be singular if the configurations of all five limbs are identical
as shown in Fig. 3(a). Under such a configuration, the five reciprocal screw $
r2
with zero-
pitch of five limbs are distributed on a single hyperboloid of one sheet. Since the rank of
screws on a hyperboloid of one sheet with one current is three, so the rank of constraints
exerting on the movable platform is not six but four when all actuators are locked. That
means the movable platform can still move after locking the actuators, and it is the second

class of singularity in ref. (Gosselin & Angeles, 1990). To avoid such a singularity, the
kinematic pairs which are not mounted on the base or movable platforms should be
assembled with a little difference. For example, two limbs can be assembled in another
current as shown in Fig. 4. This method is valid for currently existing 5-DoF FSPMs.
Feasible Human-Spine Motion Simulators Based on Parallel Manipulators

501


Fig. 4. Assembly condition for singularity avoidance
2.2 5-(RRR)RR

Although 5-(RRR)RR
has a different structure with 5-RRR(RR), they have the similar
constraint relationship, that is constraint screw of five limbs are the same. Hence, the
mobility of 5-RRR
(RR) is analyzed here in a simple way. In the similar coordinate frame in
Fig.3(b), the reciprocal screw of five limb screw systems for 5-(RRR)RR are the same which
form a common wrench $
r1
= [0,0,1; 0,0,0] constraining the translation along z-axis. The
manipulator is the same with 5-RRR(RR) after locking all actuators, which means movable
platform is fixed when all five actuators are locked at general configuration. Hence, base-
actuator mode is valid for the manipulator 5-(RRR)RR
.
2.3 5-(RRR)(RR)

(a) (b)
Fig. 5. 5-(RRR)(RR)
For a 5-(RRR)(RR) manipulator, the movable and base platforms are connected by five

identical limbs each also with five revolute joints. Axes of three revolute joints adjacent to
the base platform (R
1
,

R
2
,

R
3
) intersect at a point O
1
. The other two (R
4,
R
5
) intersect at
another point O
2
. Let O
1
be the origin, the x-axis be along the axis of R
1
and z-axis be
Parallel Manipulators, Towards New Applications

502
perpendicular to the base platform. In such a coordinate frame, the reciprocal screw of the
screw system is a wrench with zero-pitch

$
r1
= [O
2
; 0,0,0] (3)
whose axis passes through both O
1
and O
2
. The five reciprocal screws of five limbs are the
same. So these constraints exerting on the movable platform form a common wrench with
zero-pitch which constrains the translational freedom along a line passing through O
1
and
O
2
. So the movable platform has three rotational and two translational freedoms. As all
actuators are locked, the screw system changes to be
$
2
= [S
2
; S
02
] = [l
2
,m
2
,n
2

; 0,0,0]
$
3
= [S
3
; S
03
] = [l
3
,m
3
,n
3
; 0,0,0]
$
4
= [S
4
; S
04
] = [l
4
,m
4
,n
4
; O
2
× S
4

]
$
5
= [S
5
; S
05
] = [l
5
,m
5
,n
5
; O
2
× S
5
] (4)
The reciprocal screws for the screw system in Eq.(4) are

$
r1
and $
r2
shown in Fig. 5(b). The
axis of $
r2
is the intersection of two planes P
R2R3
and P

R4R5
. The parameter equation for the
axis of $
r2
is
N
1
· [x-x
o1
, y-y
o1
, z-z
o1
] = 0
N
2
· [x-x
o2
, y-y
o2
, z-z
o2
] = 0 (5)
where N
1
and N
2
denote the normal vector of the plane P
R2R3
(N

1
· S
2
= N
1
· S
3
= 0) and plane
P
R4R5
(N
2
· S
4
= N
2
· S
5
= 0), respectively. Similar to the 5-RRR(RR), five $
r2
and $
r1
are six
linear independent screws. So the selection of base actuators is feasible.
Note that, there is a obviously difference between the 5-(RRR)(RR) with the other two
manipulators. For 5-RRR
(RR) and 5-(RRR)RR, the constrained translation is always along
the z-axis under different configurations. However, for the manipulator 5-(RRR)(RR), the
direction of constrained translation is different under different configurations. As shown in
Eq.(3), it always passes through O

1
and O
2
. The characteristic makes it be unique in
currently existing 5-DoF FSPMs.
3. Prototype
A prototype is manufactured to verify the kinematic analysis and comparing the motion
capacity of a human-spine and the prototype (Zhu, 2007). Considering that it is easy to
guarantee parallelism than intersection at a common point in machining, 5-RRR
(RR) is
adopted as the manipulator prototype.
3.1 Structure
As mentioned in section 2.1, the axes for three joints adjacent to the base in one limb are
parallel and the other two intersect at a common point. For the convenient to guarantee the
machining accuracy, the prototype structure parameters are designed with special values.
The axes of three joints adjacent to the base are designed to be perpendicular to the base
Feasible Human-Spine Motion Simulators Based on Parallel Manipulators

503
platform to guarantee the parallelism. The axis of R
4
is perpendicular to that of R
3
. Five arc
links are manufactured through cutting a cylindrical ring averagely after drilling ten holes
with indexing plate. One big and 15 small hole are drilled for lightening the movable
platform. To avoid actuator singularity mentioned in section 2.1, limb are assembled as
shown in the Fig. 4

Fig. 6. 3-D model of the prototype

Diameters for movable and base platform are 109mm and 200mm. The length of both links
connecting joints R
1
and R
2
, R
2
and R
3
are 44mm. To allow each arc-link rotate around axis
of R
5
freely, the radian of the arc-link is 24 degrees. Five stepper motor controlled by a
motion control card actuate five R
1
, respectively. The minimize step of the stepper motor is
0.018 degree under the cooperation with motion control card.
3.2 Reachable workspace



Fig. 7. Translation and rotation simulation of the prototype
Parallel Manipulators, Towards New Applications

504

Fig. 8. Translation of prototype


Fig.9. Rotation of prototype

According to the simulation, the reachable positions form a circle similar with a pentagon.
The max translational distance is 89 mm, 44.5% of the diameter of the base. However, the
max translation of the prototype is about 75mm because of interference. The rotation angles
of the prototype around x-axis, y-axis and z-axis are 48, 48 and 66 degrees which is similar
with the simulation. The motion of a spine is mainly realized by cervical spine, thoracic
spine and lumbar spine. Considering rotation ability, cervical spine is the strongest (123, 61
and 77 degrees); the lumbar spine is the weakest (74, 29 and 9 degrees). Comparing with the
three parts of human spine, the rotation ability of the prototype is similar to the thoracic
spine, whose rotation angles are 76, 76 and 71 degrees, respectively.
Feasible Human-Spine Motion Simulators Based on Parallel Manipulators

505
5. Future work
Although mobility and kinematical performance closed to isotropy are realized through 5-
DoF FSPM with base-actuator, there are still several aspects to be improved for further
simulation capacity for the spine motion.
(a) Enlarge the reachable workspace. The reachable workspace of the prototype is smaller
than that of human spine except the rotation around z-axis (yaw). Such a problem may be
solved by rearranging the five R
4
. Immature hypotheses include, 1. arranging them in both
sides of the movable ring platform, such as two inside and three outside; 2. Control link
connecting R
3
and R
4
rotating within 180 degree instead of 360 degree through better
trajectory plan to prevent link interference, which may enlarge the rotation angles around x-
axis and y-axis to about 96 degree.
(b) Reaction time. The manipulator structure should be redesigned to ensure and improve

the reaction time of the manipulator.
(c) Mechanics analysis. As mentioned in the literature, spine for human being may work
under passive mode, in which passive force and torque should be calculated and evaluated
under outside load. Hence, to simulate the bio-mechanics, static and dynamic behavior
should be researched.
(d) Simulate with 5-(RRR)(RR) to make use of its unique characteristic.
6. Conclusion
Considering the characteristics of a human spine including nearly isotropic kinematical
performance, fast speed, available under both active and passive modes and reachable
workspace, three 3R2T 5-DoF fully-symmetrical parallel manipulators with base-actuator,
including 5-RRR
(RR), 5-(RRR)RR, 5-(RRR)(RR) are adopted as feasible human spine motion
simulators. To decrease machining difficulty and guarantee the machining precision, 5-
RRR
(RR) is designed and manufactured as the prototype of spine motion simulator. After
comparing reachable workspace of the prototype and that of human spine, the future work
are planned for further improving simulation capacity of the prototype.
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