=Paper=
{{Paper
|id=Vol-1484/paper21
|storemode=property
|title=Design, Simulation and Implementation of a 3-PUU Parallel Mechanism for a Macro/mini Manipulator
|pdfUrl=https://ceur-ws.org/Vol-1484/paper21.pdf
|volume=Vol-1484
|dblpUrl=https://dblp.org/rec/conf/iros/MaPAHH15
}}
==Design, Simulation and Implementation of a 3-PUU Parallel Mechanism for a Macro/mini Manipulator==
https://ceur-ws.org/Vol-1484/paper21.pdf
Design, Simulation and Implementation of a 3-PUU Parallel
Mechanism for a Macro/mini Manipulator
Zheng Ma, Aun-Neow Poo, Marcelo H. Ang Jr , Geok-Soon Hong, and Feng Huo,
Abstract— Parallel mechanisms have the advantages of high involved continuous contact between the robot end-effector
rigidity, high precision and fast movement in its workspace. It is and the workpiece, and the simultaneous control of the force at
a most suitable mechanism to serve as the mini manipulator in a the point of contact. Such force/position controlled operations
macro/mini manipulator as the mini manipulator needs to have include high-precision edge and surface finishing operations
fast response and high resolution in positioning. In this paper, often encountered in the precision engineering, aerospace, and
the design of a 3-PUU parallel mechanism to be used as such a marine industries.
mini is presented. Failures are encountered during the process of
simulation and implementation of the parallel mechanism. Since an adequate workspace and a sufficient
Causes of the failures are analyzed and solutions are proposed to payload-carrying capacity are required in the performance of
overcome these. Based on the lessons from building the first their tasks, industrial robots are often designed with long and
prototype, improvements were made to the second prototype large arms. With its large mass and inertia [1], it is thus
which effectively removed the shortcomings resulting in a mini difficult to control such a single robotic arm in applications
which met the requirements for its intended application. which require position, force or force/position control and
achieve high accuracy with a fast response simultaneously.
I. INTRODUCTION
A proposed solution is to implement a compact
The development and application of robotics has made
end-effector with a small limited workspace which can have a
much progress since the first programmable industrial robotic
high bandwidth and high accuracy in positioning and have this
arm, the Unimate, was invented in 1961. Compared with
carried by a larger but slower robotic arm. This configuration
human operators, industrial robots have the advantages of high
is commonly referred as a macro/mini manipulator, where the
precision, repeatability and speed of motion, and high
large robotic arm is referred to as the “macro”, and the smaller
dexterity. They can also work in environments hazardous or
and faster end-effector referred to as the “mini”. The
unsuitable for human beings and, with large robots, are capable
macro/mini manipulator has the advantages of a large
of carrying and moving, with higher speeds and accuracy of
workspace provided by the macro robotic arm, as well as a fast
motion, heavy workpieces. In addition, except for downtime
and high-accuracy response provided by the mini [2].
for maintenance, they are 24/7 workers who do not need rest or
holiday leaves and can thus improve productivity and speed of Considerations which need to be taken in the design of a
production. mini manipulator depend on what tasks it is being developed
for. In this paper, a mini manipulator designed for polishing
When used appropriately, industrial robots can reduce the
and deburring tasks is discussed. The normal forces that need
need, not only of unskilled labourers but also skilled workers,
to be applied by the polishing or deburring tool on the
in industry. As a result, they have found widespread
workpiece are estimated at up to 100 N and a few Newtons for
applications in repetitive operations such as material handling
polishing and deburring respectively. The optimum exerted
and assembly, welding and spray painting. To date, most of the
force depends on the type of operation, the material of the
applications of industrial robots are for non-continuous contact
workpiece and the type of tool used. A rough
type of operations, operations which do not require the robotic
sanding/polishing operation using a sanding/polishing pad
end-effector to be in continuous contact, and with a controlled
which has a large area of contact with the workpiece surface
level of contact force, with the workpieces.
will require a large exerted force whereas a small exerted force
Recent advances in robotics technology have allowed the will be needed for a fine finishing operation with a smaller
development of robotic arms with increased speeds and polishing pad.
precision of motion and with greater build-in intelligence.
The profile of the surface of the workpiece that is to be
There is now increasing interest in developing and employing
operated on is assumed not to have sudden rapid changes such
these devices for more challenging tasks, including those
that a workspace in the form of a sphere with a diameter of
labour-intensive and low-productivity operations which
40mm will be sufficient for the mini end-effector. During a
polishing or deburring operation, the macro manipulator
*Research supported by SIMTech-NUS Joint Laboratory and A*STAR. carries the mini manipulator (end-effector) along a desired
Zheng Ma is with the Advanced Robotics Center and the SIMTech-NUS reference path parallel to and at a small distance away from the
Joint Laboratory (Industrial Robotics), National University of Singapore, surface to be polished or from the edge of the workpiece to be
Singapore, 117580. (Corresponding author. Phone: +65-91188562; Email: deburred. For optimum operation, the orientation of the
mpemz@nus.edu.sg).
end-effector should have a predefined orientation with respect
Aun-Neow Poo, Marcelo H. Ang Jr, Geok-Soon Hong and Feng Huo are
with the Department of Mechanical Engineering, National University of to the surface, or edge, of the workpiece. While being moved
Singapore, Singapore, 117576. (Emails: mpepooan@nus.edu.sg, along this reference path by the macro, the mini moves in such
mpeangh@nus.edu.sg, mpehgs@nus.edu.sg and huofeng@nus.edu.sg).
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The path to success: Failures in Real Robots October 2, 2015
a way as to exert the desired normal force on the workpiece. prismatic joints move in a direction perpendicular to the base
Since the mini is always in contact with the surface or edge of platform and are attached symmetrically at 120 degrees apart at
the workpiece, and as long as there are no sudden and large Ai , where i 1,2,3 , to the base platform. As shown in Fig. 1,
change to the surface or edge of the workpiece, the workspace
of the mini will not need to be large to perform the polishing or two universal joints (universal joints) connect the end of each
deburring task. prismatic joint to the top platform. The axes of the two
universal joints are parallel to each other and perpendicular to
Based on the aforesaid considerations and using feedback the prismatic joint. According to the Chebychev-Grübler–
from users with experience in polishing and deburring Kutzbach criterion [3], the number of degrees-of-freedom is
operations, a 3-DOF PUU(Prismatic-Universal-Universal) given by:
parallel mechanism, inspired by the Delta robot was selected j
for the mini manipulator. This 3-DOF translational parallel M 3(N 1 j) fi
mechanism (TPM) has only pure translational motions and was i1
designed to have a cylindrical workspace with a diameter of where N is the total number of links, j the total number of
40mm and a height of 30mm. joints, and fi , ( i 1,2,3 ) the degrees of freedom of link i . For
In the design process, solid models were first created to the mechanism shown in Fig. 1, the total number of links
simulate and to analyze the motions, and to evaluate the (including the base link) is N 8 , the total number of joints
stresses and deformations in the various links and components is j 9 , and the degree of freedom is fi 1 for the prismatic
when it is subjected to the maximum design applied forces and joints and fi 2 for the universal joints. Thus
torques. During the simulation study of its motions,
unexpected motions with extra degrees of freedom were M 3(8 1 9) 31 6 2 3
observed which caused the mini manipulator to take on and the mechanism shown in Fig. 1 has three
postures in which the platform on the mini end-effector was degrees-of-freedom with all being translational motions as will
not purely translated but was rotated from its starting position. be elaborated on in the next section. This ensures that the top
A kinematic analysis based on the 3-DOF translational motion platform is always parallel to the base platform.
fails to explain these unexpected motions since the
assumptions made in the kinematic analysis does not hold top platform U‐ joint
when the mechanism is not in parallel with its starting position. B3 B2
P3 O’
To reduce the overall cost and time, the universal joint U‐ joint
P2
components are directly ordered off the shelf for
implementation. The parallel mechanism appears to have B1
Prismatic
notable backlash. The resulting precision of the mechanism is joint
poor and cannot serve as the mini manipulator which supposed base platform P1
A3 A2
to have high accuracy in positioning.
The mechanism is modified eventually to overcome the O
backlash problem and retains the same kinematics as
previously designed. As a result, the working range and
mobility of the mechanism meets the requirement. Together
with a proper control algorithm, the mechanism can be used to
serve as the mini manipulator which has a fast response and A1
high precession in positioning.
In this paper, the 3-PUU parallel mechanism is first Figure 1. Structure of the 3-PUU parallel mechanism.
described and a standard kinematic analysis is derived under
assumptions. Unexpected motions in simulations are shown,
with a brief analysis of the reason why it happens. Problems of
backlash and positioning accuracy encountered in
implementation is discussed with an analysis of an
off-the-shelf universal joint structure. Improvements of the
mechanism architecture and joint options are presented which
overcomes the failure from the simulation as well as the real
implementation.
II. MECHANISM DESCRIPTION AND KINEMATIC ANALYSIS
A. A 3-PUU Parallel Mechanism
The structure of the 3-PUU parallel mechanism designed is
shown in Fig. 1 with three identical limbs connecting the base
platform to the top platform. Fig. 2 shows the structure for one
of the limbs. From the figures, it can be noted that the three Figure 2. One of the limbs of the 3-PUU parallel mechanism.
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B. Kinematic Analysis of 3-DOF Translational Motion z i L2 ( x xi ) 2 ( y yi ) 2 z
With knowledge of the 3-DOF translational mobility, the
kinematic model of the parallel mechanism can be derived [4]. In the same way, the forward kinematics can be obtained
The top view of the base and top platform is shown in Fig. 3, by applying the same constraint equation.
where Ai and Bi are the locations where the prismatic joints and
the universal joints are mounted to the base and the top III. FAILURES IN SIMULATION AND IMPLEMENTATION
platform respectively. Coordinate Frame O and Frame O’ are
With the kinematic model obtained, the parameters R, r and
respectively attached at the centre of the base and the top
L were chosen to meet the workspace criteria. Solid models
platform. The distance from the center of the platforms to Ai
were then established for motion and stress analysis, the
and Bi are R and r respectively. Let the displacement of the ith
former to confirm the translational motions of the top platform
prismatic joint attached at Ai be zi. All the universal joints are
within the specified workspace and the latter for sizing the
passive.
components for strength and stability.
Since the parallel mechanism are constrained to have only
translational motions, the transformation matrix for rotation During simulation, some unexpected results were observed
from frame O’ to frame O is an identity matrix. Let the position when the top platform moved away from being parallel to the
vector of Frame O’ in Frame O be base platform. Unacceptable motion performance was also
obtained with the first prototype developed using off-the-shelf
[ c ]O ( x y z )T universal joints. These will be discussed in the following
A2 sections.
B2
A. Extra DOF observed in Simulation
R Solid models of the parallel mechanism were created using
r the software SolidWorks®. Motion studies were done
A3 B3 simulating motion at the three prismatic joints. This caused the
three lower universal joints, P1, P2, and P3 in Fig. 1, to move
vertically. Various combinations of linear motions for the three
prismatic joints were used to study the movement of the top
platform relative to the base platform, as well as to verify the
B1 size of workspace of the parallel mechanism.
A1
The top platform was expected to remain parallel to the
base platform at all times since the design of the mechanism
Figure 3. Top view of base platform(left) and top platform(right). constrained it to have only 3-DOF translational motion.
However, it was noted that for some motion combinations of
According to the mechanism structure shown in Fig. 1 and the prismatic joints, the top platform does not always remain
the geometric conditions shown in Fig. 3, the inverse and parallel to the base platform but moved into a non-parallel
forward kinematics of the parallel mechanism can be obtained. mode of motion after remaining parallel for some time. Fig. 4
By assuming the top platform has only translational motion shows an example of how the roll-pitch-yaw angles of Frame
with respect to the base platform, position vector Bi in frame O’ with respect to Frame O change with time for one such
instance. From the figure, it can be seen that the top platform
O’ is
moves with only translational motion for about 11s after which
[ Bi ]O ' (r cos i r sin i 0)T , it has rotational motions.
1 30 , 2 150 , 3 90
Therefore the position vector Bi in frame O is
[ Bi ]O (r cos i x r sin i y z )T
and the position vector Pi in frame O is
[Pi ]O (R cosi R sini zi )T
For all three limbs, if the distance between the two universal
joints, Bi to Pi is L. The constraint equation can then be written
as
[Bi Pi ]O L
After substituting Bi and Pi into (7), we have
( x xi ) 2 ( y yi ) 2 ( z zi ) 2 L2 ,
xi ( R r ) cosi , yi ( R r ) sin i Figure 4. Roll-pitch-yaw angles oftop platform for non-paralle motion.
The inverse kinematics thus can be obtained as
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To explain the unexpected rotational motion, the a hole to accommodate the external shaft and a dowel pin is
assumption of pure translational motion was reviewed. A used to hold the shaft to the joint as shown in the figure.
typical drawing of a universal joint is shown in Fig.5.
Ux
Uy
Figure 6. Universal joint(double) [7].
Link side
UzP
Figure 7 shows the first prototype of the mini manipulator
Platform UzL mechanism using these universal joints. Three linear actuators,
side labeled with 0, 1 and 2, are used for the prismatic joints. Each
link connecting the prismatic joint to the top platform is made
up of a circular shaft with a universal joint at each end. The
universal joint at one end of each link is fixed to a linear
actuator and the other end to the top platform.
Figure 5. Rotational axis of a universal joint.
Consider one of the three universal joints attached to the
top platform as shown in Fig. 5. With the other end, Pi, of the
link fixed, there will be no rotation about the axis UzL, The
universal joint can only rotate about the Ux and Uy axes,
enabled by the cross component in the joint. With only two
degrees-of-freedom, there will not be any rotation about the
axis UzP, and thus no rotation of the platform [5].
Since there are three universal joints attached to the top
platform, therefore no rotation of the platform is allowed about
three axes. When these three axes are linearly independent
in 3 , the top platform will lose all the rotational motion and Figure 7. Translational parallel mechanism using U-joints.
its 3-DOF motions will be purely translational. Based on this
analysis, the rotational motion of the top platform during When the three linear actuators are fixed in any position,
simulation as shown in Fig. 4 is thus unexpected. i.e. not moving, the top platform should also remain in a fixed
position parallel to the base platform. However, it was found
This rotational motion observed in simulation is suspected that with the actuators fixed in their positions, the horizontal
to be caused by the loss of independence among the three axes slack of the top platform was 4 to 5 mm, which is unacceptably
UzPi. When two or more axes become linearly dependent, the large, together with unacceptably large angular rotations.
parallel mechanism will be in a singular position. Unlike the Investigations showed that these unacceptably large motions,
singularities in serial-link robots, instead of losing degrees of or “backlash”, are due to the clearances used in the
mobility, a parallel mechanism gains extra degrees of freedom manufacture of the mechanical components used. While pure
at a singular position [6]. translation motion of the top platform was observed in
In Fig. 4, it is likely that the parallel mechanism reached a simulation for which perfect dimensions of the various
singular position at about 11s, gained an extra degree of components are used in computation, such perfectly formed
rotational mobility and the top platform became non-parallel to parts are not available in practice, thereby resulting in the
the base platform. Thereafter, the motion of the mechanism unacceptable results. A close examination of the first prototype
was no longer constrained to be purely translational. showed that the exhibited backlash phenomenon is due almost
entirely to clearances in the off-the-shelf universal joints used.
Referring to the Chebychev-Grübler–Kutzbach criterion,
the mechanism should have three degrees-of-freedom when it The universal joint, also known as a Hooke's joint, is a joint
is not in a singular position. It is likely that the motion of the or coupling which is commonly used to transmit rotary motion
mechanism after passing through the singular position is a from one rigid shaft to another rigid shaft when the axes of the
combination of three degrees of motion with both rotation and two shafts are at a small angle to each other. The rotary motion
translation. Further investigation will be needed explain and to transmitted is usually in one direction only. Because there is no
understand this unexpected simulation result. change in direction of the transmitted rotary motion, the small
clearances designed into them for ease of manufacture does not
B. Backlash in Implementation cause any backlash problem.
The universal joints used in the construction of the first The universal joints used in the TPM mechanism in the
prototype were off-the-shelf good quality joints the schematic work here serve a different purpose. They serve as joints
of which is shown in Fig. 6. Each side of the universal joint has providing two degrees of freedom (rotary motion) constraining
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The path to success: Failures in Real Robots October 2, 2015
the motion of the parallel mechanism as required from the are used for their typical functions of transmitting rotary
structure shown in Fig. 1. Referring to Fig. 5, the universal motion between two shafts.
joints used should rotate only about axes Ux and Uy to cause The first prototype failed to meet the requirements for its
the top platform of the TPM mechanism to move. There should intended application and a review of the design, and where it
be no rotation about axis UzL or UzP. However, when one side
failed, was carried out to come up with the second prototype.
of the U joint, say the link side, is fixed and not allow to rotate
about its axis UzL, it is observed that the other side has freedom IV. LEARNING FROM THE FAILURES
to rotate, about axis UzP, to some significant degree. This is
due to manufacturing clearances designed into the joints, in In the process of developing and building the first
particular at the four ends of the cross component in the joint. prototype, two valuable lessons were learned. One is the
The resulting free-play or backlash is accentuated due to the unexpected results during simulation studies and the other is
short lengths of the two rods forming the cross component in the poor performance in the fabricated mechanism due to
the joint. The off-the-shelf U joints thus did not have sufficient manufacturing clearances and backlash in the off-the-shelf
stiffness along the Uz axes and are not suitable for the TPM universal joints used.
mechanism.
It is noted that that the top platform of the mechanism does
Another significant cause of the free-play or backlash not remain parallel to the base platform under all
problem in the motion of the TPM mechanism is due to circumstances. Rather, when starting from a parallel position,
clearance applied during the fabrication of the mechanism. As the top platform may move into a mode, or region of its
mentioned earlier and with reference to Fig. 6, dowel pins were workspace, where it gains rotational motions after passing
used to connect the external shaft to each end of the U joints. through a singular position. This problem occurred during
Ideally, the two holes in the U joint and the one in the shaft to simulation when it is put all possible motions within its total
accommodate the dowel pin should all be of exactly the same workspace. In practice, this problem can easily be overcome
diameter, corresponding to the diameter of the dowel pin, with by constraining the motions of the three actuators such that its
their centers perfectly aligned. However, as the holes were workspace clearly does not contain any singular positions.
drilled at different times, if they were to be made of the same
diameter with very little clearance, the centers of the holes The first prototype has unacceptably poor accuracy in its
need to be perfectly aligned in order for the dowel pin to be motion and positioning. The top platform has some degrees of
inserted. Alignment of the holes, when drilled separately, is not mobility, of about 5 mm due to backlash when the actuators are
easily done. As such, the fabricator introduce some clearance fixed in their positions. This mobility is not acceptable as the
and made the hole in the shaft larger (Fig. 8) than that of the mini manipulator is required to have high stiffness and
holes in the U joint, which is of the same diameter as the dowel precision. It is clear that this problem is caused by the
pin. While this allowed for the insertion of the dowel pin even manufacturing clearances in the off-the-shelf universal joints
if there is some slight misalignment of the holes during used. To overcome this problem, while still using lower-cost
manufacture, it caused significant rotational free-play or off-the-shelf components, other type of joints which has the
backlash between shaft and the universal joint. Here again, the same motion properties as universal joints but do not suffer
rotational backlash is accentuated by the small diameter of the from the same backlash problem was investigated as
shaft, and thus the length of the hole in it. replacements.
The mechanical structure to replace the link with its pair of
universal joints is shown in Fig. 9. It is composed of four ball
joints connected in a way to form a parallelogram.
B
A
D
C
Figure 8. Clearamce between dowel pin and the external shaft connected to
the U-joint. Figure 9. Improved parallel mechanism with ball joints.
The unsatisfactory motion of the first prototype of the According to the property of an ideal parallelogram, the
mechanism is largely due to the clearances in the off-the-shelf opposite sides of the parallelogram will always be parallel.
universal joints and the limited machining accuracy of the Therefore, the side AB will always be parallel to the side CD in
fabricated parts. Information on clearances for off-the-shelf Fig. 9. Since the side CD is mounted parallel and fixed to the
base platform, the side AB will also always be parallel to the
universal joints are not readily available from manufacturers
base platform. As there are three limbs in the TPM mechanism,
as such information may not have been important when they
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there are three parallelogram with three sides AB attached to resolved. Further research will be done to determine the exact
the top platform. cause of the rotational motions of the 3-PUU parallel
These three parallelogram limbs are attached to the top mechanism during simulation.
platform such that the three sides AB all lie in a plane and the Unacceptable free play and backlash was exhibited by the
top platform is parallel to this plane. Since all the three sides first prototype. This was not evident in the simulation
AB are parallel to the base platform, the plane formed by them experiments which are based on perfectly manufactured
will be parallel to the base platform. Therefore, the top components. Investigations showed that this problem was due
platform will also always be parallel to the base platform. With to inaccuracies in the dimensions of the components used. The
the top platform constrained to be parallel to the base platform, main cause was the free play in the off-the-shelf universal
and the base platform is fixed and immobile, the motion of the
joints used for the first prototype. To overcome this problem
top platform will be constrained to be translational only.
the universal joints were replaced by off-the-shelf ball joints
If there is free play or backlash in the ball joints at A, B, C, forming a parallelogram structure for the three limbs of the
or D in Fig. 9, then the parallelogram formed will not be an mechanism. The kinematic model of the mechanism remains
ideal parallelogram. In this case, the sides AB may become the same but the free play problem was effectively eliminated
non-parallel to the side CD. The amount of non-parallelism
and the second prototype exhibits high stiffness and
depends on the amount of free play in the ball joints and the
length of the sides AB and CD, the longer the sides are, the positioning accuracy.
smaller the degree of non-parallelism. Lessons were learned from unexpected outcomes and
failures during the simulation experiments and in
For the typical applications they are intended for, good implementation. Properly designed simulation experiments
quality ball joints have almost no free play or backlash. The
may produce results not predicted by theoretical studies as
length of the sides AB and CD of the parallelogram are also
much longer than the length of the cross component in the these studies are normally based on certain simplifications
universal joints. As such, the use of ball joints with a and assumptions, which cannot be completely replicated in
parallelogram structure for the three limbs of the TPM simulation experiments.
mechanism effectively eliminated the free play and backlash Furthermore, straightforward simulation experiments
problem. The resulting second prototype is rigid and has high which are based on perfect physical properties of the
precision in positioning. With the actuator fixed in their component parts may not show up possible inadequacies in
positions, there is no measurable backlash in the top platform. the design. These inadequacies may show up only in the
The backlash found in the first prototype had been effectively prototypes built due to unavoidable imperfections in the
eliminated and this second prototype will be suitable as the physical components making up the whole system.
mini in a macro-mini manipulator to be used for finishing and
deburring applications for which both position and
force/position control are required. Unlike a serial-link robot, ACKNOWLEDGMENT
the parallel structure of this robotic device gives it the high The authors acknowledge the support from the Collabora-
rigidity and thus the capability of exerting large forces on the tive Research Project under the SIMTech-NUS Joint Labora-
workpiece in force-controlled polishing applications tory (Industrial Robotics). This work was also supported in
part by the Science and Engineering Research Council
V. CONCLUSIONS (SERC) A*STAR Industrial Robotics Program Grant 12251
A parallel mechanism, based on the structure of the Delta 00008.
robot, was designed and implemented to serve as a mini REFERENCES
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