A six degree of freedom structure forming a robotic manipulator, consisting of two five-bar linkages (30 and 80) set on rotatable base linkages (18 and 58); the output points (44 and 94) of the five-bar linkages (30 and 80) are attached to a rigid payload platform (48) by universal joints (46 and 96), respectively. Each linkage (30 and 80) on its rotatable bass can position its output point in three degrees of freedom, but since the two five-bar linkages (30 and 80) are tied together at the platform (48), five degree of freedom motion of the platform (48) results--three degrees of freedom in translation, and two of rotation. A seventh motor (100), mounted for example on one of the five bar linkages, provides power to rotate the platform about the axis defined by the two universal joints (46 and 96). The rotational torque is coupled through one of the universal joints (46 or 96).

TECHNICAL FIELD 
This invention relates to robotic manipulators in general and in particular 
to such manipulators having all but one drive actuator attached to the 
parts of the linkage near the base so as to impart high resolution and 
high stiffness motion to a platform in six degrees of freedom. 
BACKGROUND ART 
Many attempts have been made to design mechanisms for the six degree of 
freedom (6-DOF) control of a moveable platform. The applications have been 
diverse, from machine tool positioning to realistic force-reflecting 
master hand controllers. 
Stewart Platform 
One of the oldest mechanisms for platform control is the Stewart platform 
(Stewart D., 1965, "A Platform with Six Degrees of Freedom", Proceedings 
of The Institution of Mechanical Engineers, London, England, Vol 180, pp 
371-386). It is in wide use for heavy-lift applications such as aircraft 
simulators. Six struts are used to join a suspended platform to its base; 
they lie along the edges of an octahedron, to give a highly symmetric 
arrangement. Each strut contains a prismatic (sliding) actuator, and is 
connected to the base by a universal joint (two orthogonal intersecting 
revolute joints) and to the platform by a spherical joint (three 
orthogonal intersecting revolute joints). 
Crossed-strut Stewart platform 
Staughton and Arai (Stoughton R. & Arai T., 1993, "A Modified Stewart 
Platform Manipulator with Improved Dexterity", IEEE International 
Conference on Robotics and Automation) suggest an improvement over the 
Stewart platform, created by allowing the struts to cross over one 
another, and attach at more distant points on the base and platform. Three 
struts are mounted with their end points on an outer circle, with the 
intervening three on an inner circle. The longer struts are closer to 
horizontal, giving improved force capacity in the plane parallel to the 
base and increased torque about a normal to the base. 
Arai et al (Arai T., Stoughton R., Homma K., Adichi H., Nakamura T. & 
Nakashima K. 1991, "Development of a Parallel Link Manipulator", IEEE 
International Conference on Robotics and Automation) describe a modified 
Stewart platform with six struts crossed over to give near-isotropic force 
and moments, with some workspace limitations. The application is an 
underground excavation task. 
Six-Arm Design, with Serial Linkages in Each Arm. 
Pierrot et al (Pierrot F., Dauchez P. & Fournier A., 1991, "HEXA: A Fast 
Six-DOF Fully-Parallel Robot", IEEE International Conference on Robotics 
and Automation) describe a design with six independent articulated arms 
supporting a plate hanging below a base. The arms are arranged in pairs in 
order to simplify the arrangement of actuators; each arm is driven by a 
rotary actuator at the shoulder that alters the arm's pitch. 
Triple Arm Designs, with Serial Linkages in Each Arm. 
Cleary and Brooks (Cleary, K. and Brooks, T., 1993, "Kinematic Analysis of 
a Novel 6-DOF Parallel Manipulator", IEEE International Conference on 
Robotics and Automation, Atlanta, Ga., pp. 708-713) present a 6-DOF device 
combining three 2-DOF linkages. Driven by a pair of motors through a 
differential gear, each linkage can be rotated in pitch and roll to steer 
the suspended platform. 
Triple Arm Designs, with Five-Bar Linkages in Each Arm. 
Iwata (Iwata H., 1990, "Artificial Reality with Force-feedback: Development 
of Desktop Virtual Space with Compact Master Manipulator", SIGGRAPH, 
Dallas, Tex., Vol. 24, No. 4, pp. 165-170) built a 9-DOF device that 
provides 6-DOF motion to the hand and 1-DOF motion to each of three 
fingers. The main platform motion is provided by three pantographs 
(five-bar linkages with zero length base member) connected by universal 
joints (U-joints) to the corners of the triangular platform. Each 
pantograph is driven by two rotary actuators at the base. 
Long and Collins (Long G. & Collings C., "A Pantograph Linkage Parallel 
Platform Master Hand Controller for Force-Reflection", IEEE International 
Conference on Robotics and Automation, Nice, France, May 1992, p 390) 
report a 6-DOF joystick with three parallel pantograph linkages. 
Mimura and Funahashi (Mimura, N. and Funahashi, Y., 1995, "A new analytical 
method applying 6 DOF parallel link manipulator for evaluating motion 
sensation", IEEE International Conference on Robotics and Automation, p 
227) describe a similar mechanism, with three five-bar mechanisms (with 
no-zero length base links) in place of the pantographs. Double Arm Design, 
with Serial Linkages in Each Arm. 
Iwata (Iwata H., 1993, "Pen-based Haptic Virtual Environment", IEEE 
International Symposium Conference on Robotics and Automation) presented a 
6-DOF haptic pen positioned by two 3-DOF serial manipulators. One end of 
the pen is connected to one of the manipulators by a universal joint (two 
orthogonal recolute joints with interesecting axes), while the other end 
is connected to the second manipulator through a screw mechanism and a 
universal joint. If the two robots move such that the distance between the 
universal joint centers is constant, the pen moves with five degrees of 
freedom: three in translation and two in rotation (pitch and roll about 
the pen). Changes in the distance between the two universal joint centers 
result in a yawing motion of the pen due to the screw mechanism. 
Rigid Strut Designs, with Base-Sliding Supports 
Behi (Behi F., 1988, "Kinematic Analysis for a Six-Degree-of-Freedom 3-PRPS 
Parallel Mechanism", IEEE Journal on Robotics and Automation) describes a 
robot manipulator with three rigid struts. The struts are attached by 
spherical joints to the corners of a triangular platform, and at their 
other ends to sliders which run along the sides of a triangular base. Each 
of the three sliders carries a rotary actuator, which controls the pitch 
of the strut attached to that slider. 
Hudgens and Tesar (Hudgens J. and Tesar D., 1992, "Analysis of a 
Fully-Parallel Six Degree-of-Freedom Micromanipulator", IEEE International 
Conference on Advanced Robotics) present a device with six rigid struts 
attached by spherical joints to both the platform and the base. The joints 
are equidistant from the centers of the platform and the base; the struts 
are arranged in three pairs, the members of each pair being parallel and a 
short distance apart. The base joints can be pulled or pushed (by 
actuators connected to eccentric drives) along the circumference of the 
base circle, thereby giving rise to small movement in the platform. 
A device presented by Mouly and Merlet (Mouly N. & Merlet J., 1992, 
"Singular Configurations and Direct Kinematics of a New Parallel 
Manipulator", IEEE International Conference on Robotics and Automation, 
Nice, France, pp 338-343) also has six rigid struts; these are connected 
by spherical joints at one of their ends the corners of a triangular 
platform, and at the other end (by U-joints) to moveable supports near the 
corners of a triangular base. The supports move vertically, so the end of 
each strut can rise and fall relative to the surface of the base. 
OBJECTS AND ADVANTAGES 
It is therefore an object of the present invention to provide six degree of 
freedom translation and orientation to a platform, for the purpose of 
creating a manipulator without the disadvantages mentioned in the previous 
section. 
The primary advantage is the provision of the largest possible non-singular 
workspace. A secondary advantage is the smaller number of linkages and 
pivots, resulting in less friction, backlash, mass and potential for 
collisions between linkage elements. 
An object is to produce a device having fewer geometric design parameters, 
thus easing its design for a specific application. 
Another object of the present invention is to mount motors wherever 
possible next to the fixed base, in order to reduce the inertial load. 
A further object of the present invention is to simplify the control 
computations. By allowing analytical solutions of both the inverse and 
forward kinematics, it avoids the complex control calculations that plague 
many parallel devices. 
Further objects and advantages of the hybrid serial/parallel mechanism will 
become apparent from a consideration of the drawings and the ensuing 
description.

SUMMARY 
This represents a novel application of five-bar mechanisms to 5-DOF or 
6-DOF motion. The new features are the parallel placement of the folding 
axes of rotation of the two five-bar linkages, the use of redundant 
actuation to generate the folding motion of the two five-bar linkages and 
the addition of a sixth degree of freedom by rotation of the platform 
independently of the five-bar linkages. 
Description--Main Embodiment, FIGS. 1A to 1G 
A robotic manipulator, shown generally at 10, made according to the present 
invention, is illustrated in FIGS. (1A) to (1G). Manipulator 10 includes a 
base 12 or frame upon which is mounted waist/shoulder assemblies 14 (see 
FIG. 1C) and 54; to these in turn are attached five-bar linkages 30 and 
80, which are in turn attached to either side of a platform 48 by means of 
joints 44, 46, 94 and 96 as shown in FIGS. 1F and 1G. 
Device 10 forms a six degree of freedom hybrid serial/parallel robot. 
Waist/shoulder assemblies,14 and 54, and five bar linkages, 30 and 80, 
provide five degrees of freedom, while a motor 100 mounted on five-bar 
linkage 80 and connected to the platform 48 by means of universal joint 96 
and a gear train 98 (see FIG. 1C) provides the sixth degree of freedom. 
Waist/shoulder assembly 14, shown in FIG. 1D, is composed of three motors 
16, 26 and 28, with waist link 18 driven by motor 16. The link rotates at 
one end in bearing 20 which is fixedly mounted to the base by bearing 
support 24; at the other end, the rotating shaft of motor 16 is fixedly 
attached to waist link 18, while the motor body is fixedly attached to 
base 12 by waist motor support 22. Near each end of waist link 18, motors 
26 and 28 are fixed to waist link 18 by motor clamps 27 and 29, 
respectively, (see FIG. 1D) which fixedly attach the case of the motor to 
the waist link 18. The motors 26 and 28 are oriented with their driven 
shafts at right angles to waist link 18, mutually parallel and pointing 
outward from the middle of base 12. 
Five-bar linkage 30 is composed of waist link 18 and four other linkages, 
32, 34, 40 and 42. Proximal links 32 and 34 are fixedly attached to the 
rotating shafts of motors 26 and 28, respectively. They are mounted at 
right angles to these shafts, and protrude in a direction that is 
generally away from base 12. Distal links 40 and 42 are attached to 
proximal links 32 and 34, respectively, by pin joints 36 and 38, also 
known as the elbow joints. The distal links rotate in the same plane as 
the proximal links. The two distal links, 40 and 42, are joined by a third 
pin joint 44 (see FIG. 1F), known as the wrist joint. 
The shaft of wrist joint 44 is attached to one end of a two degree of 
freedom universal joint 46, the other end of which is fixedly attached to 
one side of a disk-shaped platform 48. The shaft of wrist joint 44 is free 
to rotate independently of distal links 40 and 42. 
The other side of the overall structure, waist/shoulder assembly 54 and 
five-bar linkage 80, is symmetric with respect to the first side, except 
that tie shaft 95 of wrist joint 94 is driven by the platform motor 100. 
This half of the assembly is described in the next three paragraphs. 
Waist/shoulder assembly 54, shown in FIG. 1E., is driven by three motors 
56, 66 and 68, with waist link 58 driven longitudinally by waist motor 56. 
The link rotates at one end in bearing 60 which is fixedly mounted to base 
12 by bearing support 64; at the other end, the rotating shaft of waist 
motor 56 is fixedly attached to waist link 58, while the body of waist 
motor 56 is fixedly attached to base 12 by waist motor support 62. Near 
each end of waist link 58, shoulder motors 66 and 68 are fixed to waist 
link 58 by motor clamps 67 and 69, respectively, which fixedly attach the 
cases of shoulder motors 66 and 68 to waist link 58. The shoulder motors 
are oriented with their driven shafts at right angles to waist link 58, 
mutually parallel and pointing outward from the middle of base 12. 
Five-bar linkage 80 is composed of waist link 58 and four other linkages, 
82, 84, 90 and 92. Proximal links 82 and 84 are fixedly attached to the 
rotating shafts of shoulder motors 66 and 68, respectively. They are 
mounted at right angles to these shafts, and protrude in a direction that 
is generally away from base 12. Distal links 90 and 92 are attached to 
proximal links 82 and 84, respectively, by pin joints 86 and 88, also 
known as the elbow joints. The distal links rotate in the same plane as 
the proximal links. The two distal links, 90 and 92, are joined by a third 
pin joint 94, known as the wrist joint. 
The shaft of wrist joint 94 is attached to a two degree of freedom 
universal joint 96, the other end of which is fixedly attached to one side 
of a disk-shaped platform 48. The shaft of wrist joint 94 rotates 
independently of distal links 90 and 92, and is connected to platform 
motor 100 by means of gear train 98; this gear train, which may consist of 
internal gears or a flexible, rotating cable, permits platform motor 100 
to be placed in a convenient location on link 90. 
A handle 50 is placed on platform 48. This handle is representative of any 
number of payloads that can be placed on device 10. The handle represents 
the device's operation as a hand controller; the device can also be used 
as an active positioner. 
Operation--Main Embodiment, FIGS. 1A to 1G 
As shown in FIG. (1A), each five bar linkage (30 and 80) has three motors 
at its base--two to drive wrist joints 44 and 94 in the plane of the 
linkage, and a third to rotate the plane of the five-bar linkage about its 
base at waist links 18 and 58, respectively. (Motors 26, 28, 66 and 68 
that drive five-bar linkages 30 and 80 in their own planes are termed 
"shoulder motors" while the plane rotation, or five-bar linkage folding, 
motors 16 and 56 are termed "waist" motors.) 
The top ends of each linkage (30 and 80) are attached to the platform by 
means of universal joints 46 and 96, respectively. Each linkage (30 and 
80)) can execute motions in three degrees of freedom, but the two linkages 
30 and 80 are tied together at platform 48, so five degree of freedom 
motion results--three degrees of freedom in translation, and two of 
rotation. 
Platform motor 100, mounted on one of the five bar linkages (80), provides 
power to rotate the platform about the axis defined by the two universal 
joints 46 and 96. The rotational torque is coupled through universal joint 
96. The seventh motor is termed the "platform" motor. 
Device 10 is equivalent to two elbow manipulator arms with passive 
spherical wrists, joined at their distal ends through an actuator aligned 
with the wrist centers. 
Consider the operation of one of the five-bar linkages 30 or 80 in detail. 
The two shoulder motors 26 and 28 of five-bar linkage 30 permit wrist 
joint 44 of the linkage to be moved in the plane of linkage 30. Shoulder 
motor 26 rotates proximal link 32 about its end which is attached to the 
motor shaft, while shoulder motor 28 rotates proximal link 34 about its 
end. These rotations may occur independently; the rotations force distal 
link 40 and 42 to rotate in a constrained manner, revolving about pin 
joints 36, 38 and 44. 
The inverse and direct kinematics of this mechanism are easily computed and 
are not described here. It can be shown that the singular configurations 
of the hybrid serial/parallel manipulator occur when and only when (i) 
either of the five-bar linkages is in a singular configuration (see FIG. 
12A and 12B), (ii) the tip of a five-bar linkage intersects the axis of 
the five-bar linkage waist (see FIG. 12, #3, #4), (iii) either of tie 
five-bar linkages is at its workspace limit or (iv) the tips of the 
five-bar linkages align with a distal link of either five-bar linkage 
(this corresponds to a spherical wrist singularity). 
The five-bar linkage singularities are not particularly problematic since, 
by design, singularity 12A is eliminated if a&gt;2b, and singularities 12B, 
12C and 12D are eliminated if c&gt;(b+a/2). 
Description--Alternative Embodiments, FIGS. 3 to 4 
Alternative embodiments of the hybrid serial/parallel manipulator are shown 
in FIGS. (3) to (4), with FIG. (2), the main embodiment, redrawn in the 
same style as FIGS. (3) to (4). Joints are represented by solid round 
dots, links by straight lines between the joints, and motors, by cylinders 
with protruding lines representing drive shaft. Waist motor 56 is shown on 
the same side of base 12 as waist motor 16, rather than on the opposite 
(or back) side of base 12, but the operation is unaffected by this 
arrangement. Likewise, the view is from the front, with platform motor 102 
operating from the right; universal joint 46 therefore becomes the driven 
joint, and universal joint 96, the passive joint. 
FIG. (2) is kinematically equivalent to FIG. (1), except that gear train 98 
is removed, and platform motor 100 is replaced by platform motor 102 of 
which the drive shaft is now fixedly attached to the pin of pin joint 94. 
In FIG. (3), waist motors 56 is eliminated, since it is redundant, and 
replaced by passive joint 104. (This joint is fixedly connected to base 12 
by a support, but neither base 12 nor the support is shown in this 
symbolic illustration.) 
In FIG. (4), two waist motors (16 and 56) are again shown, but the platform 
motor is replaced by a passive mechanism (106) to rotate the platform when 
it is squeezed axially. Platform motor 102 is eliminated, and a rotation 
mechanism (106) is interposed between platform 48 and universal joint 46 
(which is now a passive universal joint, not directly driven by any 
motor). (Universal joint 46, although passive, is fixedly attached to 
distal link 40 in order to set a reference position for the platform.) 
Operation--Alternative Embodiments, FIGS. 3 to 4 
The alternative embodiment of FIG. 3 operates in the same way as the main 
embodiment, FIG. 2, except that the missing waist motor 56 forces the 
waist axis (waist link 58) to passively follow the movement induced by the 
remainder of the assembly. While there may be some loss of power in this 
arrangement, all movements throughout the workspace are nevertheless 
possible, in the following manner. 
The positions of joint 44 and universal joint 46 are fully determined by 
the action of waist/shoulder assembly 14 and five-bar linkage 30. Working 
together, these position the right side of platform 48 in space relative 
to base 12. (Shoulder motors 26 and 28 move five-bar linkage 30, and hence 
position wrist joint 44 in the plane of linkage 30, while waist motor 16 
rotates the plane of the linkage 30 about its waist link 18; that is, 
wrist joint 44, being in this plane, is moved by waist motor 16 in an arc 
centered about waist link 18.) The other end of platform 48 is located by 
the action of five-bar linkage 80. Since the length of the platform is 
fixed, then as five-bar linkage 80 moves in the plane of 80, universal 
join 96 is forced to move along a circle centered on the other universal 
joint 46, with radius equal to the distance across the platform between 
universal joints 46 and 96. Wrist joint 94, being fixedly attached to 
universal joint 96, is therefore located unambiguously in space. Wrist 
joint 94, together with the fixed locations of the end points of waist 
link 58, determines the orientation (if the plane of five-bar linkage 80, 
and hence, the angle of waist link 58 relative to base 12. In other words, 
the action of the six motors have completely determined the rotation of 
waist link 58 of the waist/shoulder assembly 54. 
Please note that, while the elimination of a redundant actuator is 
possible, the presence of the actuator has certain advantages--greater 
power, and the ability to perform self-calibration by posing the structure 
in various positions while the joint positions and joint torques are read. 
The structure of FIG. 4 is a variation built on FIG. 2, with the platform 
motor replaced by passive rotation mechanism 106. The action of this 
mechanism 106 is shown in the inset of FIG. 4. As the mechanism is 
squeezed or compressed axially, the drive shaft rotates. (This could be 
effected by a passive screw inside the mechanism, or by an equivalent 
screw formed from a recirculating ball bearing assembly.) As the mechanism 
is placed under tension, rotation in the opposite direction occurs. The 
compressive or tensile force is provided by the action of driven 
waist/shoulder assemblies 14 and 54 and five-bar assemblies 30 and 80. 
Each assembly can locate the universal joint at either end of the platform 
in three degrees of freedom. Assemblies 14 and 30 control the position of 
wrist joint 44 and hence universal joint 46, fixedly attached to wrist 
joint 44, while assemblies 54 and 80 control the position of wrist joint 
94 and hence the position of universal joint 96, which is fixedly attached 
to wrist joint 94. By altering the distance between the two universal 
joints, 46 and 96, rotational mechanism 106 is moved to different 
extensions, and hence platform 48, fixedly attached to the drive shaft of 
the mechanism, is rotated. 
Description--Alternative Embodiments, FIGS. 5 to 7 
In FIGS. (5) to (7), the waist movement (the rotation of five-bar linkages 
30 and 80 about waist links 18 and 58) is produced by motors which are 
relocated to the end of waist driving assemblies 110 and 130. In FIG. (5), 
the two waist assembly motors 112 and 132 are shown side by side, fixedly 
attached to base 12. (The support are not shown in these symbolic 
diagrams, nor is base 12 itself.) Fixedly attached to the (drive shaft of 
motor 112 is a waist assembly proximal link 114; it is attached at right 
angles to the shaft, protruding in a direction that is generally away from 
base 12. Proximal link 114 is connected by a two degree of freedom elbow 
joint 116 to a distal link 118; the other end of distal link 118 is 
connected to a three degree of freedom wrist joint 120, which replaces 
wrist joint 44 of the main and alternative embodiments in FIGS. (2) to 
(4). Elbow joint 116 could be formed from a universal joint, or a ball and 
socket, or a pin joint connected to a revolute joint attached to proximal 
link 114; wrist joint 120 could be formed from a universal joint, or a 
ball and socket, fixedly attached to existing pin wrist joint 44. 
Left side waist driving assembly 130 (or waist driving assembly 1) is 
similar to right side waist driving assembly 110 (or waist driving 
assembly 2), just described. Waist assembly proximal link 134 is fixedly 
attached to the drive shaft of waist assembly motor 132; it is attached at 
right angles to the shaft, protruding in a direction that is generally 
away from base 12. Waist assembly proximal link 134 is connected by a two 
degree of freedom elbow joint 136 to waist assembly distal link 138; the 
other end of distal link 138 is connected to a three degree of freedom 
wrist joint 140, which replaces wrist joint 94 of the main and alternative 
embodiments in FIGS. (2) to (4). 
In FIG. (6), waist driving assembly 130 is eliminated, to form a unit 
generally equivalent to FIG. (3). In FIG. (7), the two waist driving 
assemblies 110 and 130 are present, but platform motor 102 is replaced by 
rotation mechanism 106 which is interposed between platform 48 and 
universal joint 46. 
Operation--Alternative Embodiments, FIGS. 5 to 7 
Waist driving assemblies 110 and 130, shown in FIGS. (5) to (7), operate in 
a similar manner to one another. Consider waist driving assembly 110 in 
FIG.(5). Waist assembly proximal link 114 rotates about the end of waist 
assembly proximal link 114 which is fixedly attached to the drive shaft of 
waist assembly motor 112. As the drive shaft is rotated, waist assembly 
proximal link 114 pushes and pulls on waist assembly distal link 118, the 
two links being attached by two degree of freedom waist assembly elbow 
joint 116. The distal link then pushes or pulls on the three degree of 
freedom waist assembly wrist joint 120. If shoulder motors 26 and 28 hold 
the five-bar linkage in one position, then as waist assembly wrist joint 
120 is pushed or pulled, the plane of five-bar linkage 30 rotates about 
waist link 18. This accomplishes the same action as performed by waist 
motor 16, in its position colinear with waist link 18 in FIGS. 1 through 4 
Note that 2-DOF waist assembly elbow joint 116 and 3-DOF waist assembly 
wrist joint 120 in waist driving assembly 110 permit five-bar assembly 30 
to move in its own plane without undue restriction imposed by waist 
driving assembly 110. At a constant rotation angle of waist link 18, 
movement of waist assembly wrist joint 120 in the plane of five-bar 30 
causes joints 116 and 120 to bend in approximately equal angles of 
opposite sign, around axes that are normal to the plane. At the same time, 
the angle of waist assembly proximal link 114 to base 12 about an axis 
which is parallel to the drive shaft of waist assembly motor 112, and the 
angle of elbow joint 116 about an axis which is parallel to the drive 
shaft of waist assembly motor 112, change in approximately equal angles of 
opposite sign, in order to accommodate any changes in the overall distance 
between waist assembly motor 112 and waist assembly wrist joint 120. 
Waist driving assembly 130 operates in an identical fashion to waist 
driving assembly 110. Waist assembly proximal link 134 rotates about the 
end of waist assembly proximal link 134 which is fixedly attached to the 
drive shaft of waist assembly motor 132. As the drive shaft is rotated, 
proximal link 134 pushes and pulls on waist assembly distal link 138, the 
two links being attached by two degree of freedom elbow joint 136. The 
distal link then pushes or pulls on three degree of freedom waist assembly 
wrist joint 140. If shoulder motors 66 and 68 hold the five-bar linkage in 
one position, then as waist assembly wrist joint 140 is pushed or pulled, 
the plane of five-bar linkage 80 rotates about its waist link 58. This 
accomplishes the same action as performed by waist motor 56, in its 
position colinear with waist link 58 in FIGS. 1, 2 and 4. 
FIG. (6) shows the hybrid serial/parallel manipulator with the waist 
driving assembly 130 removed. This is similar to the configuration of FIG. 
(3), and it operates under the same principles. By removing one redundant 
actuator, the assembly can still be moved and positioned in six degrees of 
freedom, albeit without some of the advantages of a redundantly actuated 
mechanism. 
The hybrid serial/parallel manipulator shown in FIG. (7) has both waist 
driving assemblies 112 and 132, so that both universal joints 46 and 96 
can be positioned in space with three degrees of freedom. The distance 
between universal joints 46 find 96 can therefore be varied, placing 
pressure or tension on rotational mechanism 106. The action of rotational 
mechanism 106 is to rotate in one direction when the axis is placed under 
pressure, or squeezed, and to rotate in the other direction when the axis 
is under tension. 
Comparison with Prior Art 
Parallel mechanisms have some impressive advantages and some impressive 
disadvantages over serial structures. They have better load capacity, 
stiffness, precision and inertia characteristics. These characteristics 
are due to the multiple arms which spread the load, and the normal 
practice of mounting actuators on or close to the base, rather than having 
them located at the joints and therefore carried by the linkage mechanism. 
On the other hand, they are known to have complex forward kinematics and 
smaller non-singular workspaces. Typically, the inverse kinematics are 
easily worked out in a closed form solution, but the forward kinematics 
remain a challenge for numerical methods. The workspace limitation becomes 
apparent when one considers the effect of rotating the platform about an 
axis normal to the base. At the "home" position, a large rotation angle 
can be obtained, but this angle is reduced as one nears the edge of the 
translational workspace. The singular configurations are encountered when 
a linkage inverts from its normal angle of operation, with the elbow joint 
bending the "wrong" way, for example. ("Forward kinematics" is the 
mathematical definition of end-effector or position and orientation from 
active joint angles or lengths. "Inverse Kinematics" is the mathematical 
derivation of active joint angles or lengths from end-effector or platform 
position and orientation. "Workspace" is the set of all positions and 
orientations achievable by a robot's end effector or platform. "Singular 
configurations" are individual positions and orientations within a robot's 
workspace at which the robot's behaviour is not entirely determined by the 
behaviour of its active joints.) 
The prior art falls under three main categories--Stewart platforms and 
their variants, triple five-bar supported platforms, and dual support 
devices. Stewart platforms and the triple five-bar devices will be covered 
in the next few paragraphs. The present invention falls under the dual 
support category. The only other member of this category that is known to 
the authors is Iwata's 1990 pen-based haptic device. In Iwata's device, 
the platform (a haptic pen) is supported by two serial manipulators. The 
present invention changes the 3-DOF serial (elbow) manipulators to 3-DOF 
hybrid serial/parallel supports (folding planar five-bar linkages), 
thereby imparting some of the advantages of parallel mechanisms--increased 
load-bearing potential, accuracy and stiffness, and reduced inertia. 
Moreover, the folding five-bar mechanism has the added advantage of 
excellent isotropy within its workspace. In Iwata's device, in order to 
yaw the the platform by means of the screw mechanism, the distance between 
the universal joints connected to the supporting serial robots must be 
changed. At mechanism configurations where the pen aligns with the planes 
of the supporting elbow manipulators, Iwata's mechanism is singular. In 
the present invention, the use of a separate actuator to provide the 
yawing motion is proposed. Thus seven actuators, not six, are used to 
provide 6-DOF motion of the platform. Due to actuator redundancy, 
configurations for which the platform yaw axis aligns with the planes of 
the five bar linkages are not singular. Therefore, with a seventh actuator 
for the platform yaw motion, the proposed mechanism has a substantially 
larger non-singular workspace. 
At the outset of the project, three candidates were compared in terms of 
their complexity and workspace--a prismatically actuated "Stewart" 
platform (Fischter, E. F., 1986, "A Stewart platform-based manipulator: 
general theory and practical construction", Int. J. Robotics Res., vol. 5, 
No. 2, pp. 157-182), a five-bar linkage actuated "Triple Pantograph" 
platform (Mimura N. & Funahashi Y., 1995, "A new analytical system 
applying 6 DOF parallel link manipulator for evaluating motion sensation", 
IEEE International Conference on Robotics and Automation), and a novel 
series/parallel mechanism which is the subject of this patent. Diagrams of 
the Stewart platform and the Triple Pantograph are shown in FIGS. (8) and 
(9); the hybrid series/parallel manipulator is shown in FIGS. (1) to (7), 
and is best seen for this purpose in the symbolic diagram of FIG. (2). 
The hybrid series/parallel manipulator has eleven fewer passive revolute 
joints and one less U-joint than either of the other two manipulators, 
resulting in less friction and backlash. There could be a significant 
inertial contribution from the wrist actuator, but this depends on the 
yawing torque requirements of the application. In some applications, such 
as the use of the platform as a haptic pen, very little or even a passive 
yaw degree of freedom may be sufficient, thus a light motor or just a 
bearing can be used. It should be noted that the drawback of the 
additional yawing actuator mass is partially offset by having two fewer 
base to platform linkages. By actuating and sensing the folding or "waist" 
axis of each five-bar linkage, a platform singularity is eliminated and 
the kinematics of the platform are highly simplified. The singularity that 
is eliminated occurs when the attachment points of the platform to the 
five bar linkages lie in either one of the planes of the five-bar 
linkages. 
In the following, a comparison between the workspaces of the three 
candidates are presented. For a fair comparison, the mechanisms were sized 
to have similar footprints and favorable geometries. For the Stewart 
platform, an optimization of the Jacobian matrix carried out in Lawrence 
and Chapel (Lawrence, D. A and Chapel, J. D., 1994, "Performance 
trade-offs for hand controller design", Proc. IEEE Int. Conf. Robotics & 
Automation, San Diego, Calif. pp. 3211-3216) suggests triangles for the 
base and platform, with a 2:1 base to platform ratio. With the link 
lengths approximated from the vertical range presented in Lawrence & 
Chapel, the resulting geometry is tabulated in Table 1 where q.sub.min and 
q.sub.max refer to the minimum and maximum possible lengths of the Stewart 
platform's prismatic actuators. 
TABLE 1 
__________________________________________________________________________ 
Robot Geometry 
Robot Parts 
Proximal 
Distal 
Base 
Platform 
Waist 
link link 
half- 
half- 
Strut 
Strut 
length 
length 
length 
length 
length 
min max (212 base) 
(266) 
(270) 
(210) 
(220) 
length 
length 
(254 base) 
(32, 34, 
(40, 42, 
(280) 
(276) 
(212) 
(212) 
(18, 58) 
82, 84) 
90, 92) 
(12) 
(48) 
Robot q.sub.min 
q.sub.max 
a b c L.sub.B 
L.sub.P 
__________________________________________________________________________ 
Stewart platform 
9 18 3.5 n/a n/a 2 1 
Triple Pantograph 
n/a n/a 2 8 10 2 1 
Hybrid serial/parallel 
n/a n/a 2 8 10 2 1 
manipulator 
__________________________________________________________________________ 
Next, parameters for the Triple Pantograph platform were chosen to make it 
similar to the Stewart platform. Links b and c were selected to add up to 
q.sub.max and were made similar in length to achieve good range while 
maintaining c&gt;(b+a/2) to avoid singularities. The platform remains 
identical but the base could not be made triangular as a high degree of 
linkage collisions would occur in practice. The footprint is therefore 
kept similar but a is approximately halved. 
The geometry of the hybrid serial/parallel manipulator was made identical 
to that of the Triple Pantograph platform. Its alternative architecture is 
its only distinction. 
In FIG. (10), the "semi-dextrous" workspaces of each of the three candidate 
mechanisms are displayed. A point belongs to such a semi-dextrous 
workspace if the mechanism end-point (the platform centroid) can be placed 
there and rotated .+-.30.degree. about an arbitrary orientation axis. 
The Triple Pantograph and Hybrid Serial/Parallel platforms have very 
similar workspaces which are clearly superior to that of the Stewart 
platform, which has a large void in its centre due to the constraint of 
prismatic cylinders which can, at best, retract to half of their full 
length. The superiority of the hybrid serial/parallel manipulator over the 
Triple Pantograph becomes explicit after considering a constraint of the 
U-joints that join the five-bar linkages to the platforms. Due to typical 
physical constraints and also to avoid singular positions, the U-joints 
are not allowed to exceed .+-.85.degree.. The resulting workspaces are 
shown in FIG. (11). 
In conclusion, existing six degree of freedom parallel platform robots, 
such as the Stewart Platform and a similar design which uses three five 
bar linkages, suffer from a number of drawbacks: 
restricted nonsingular workspaces, 
large numbers of design parameters (making geometric optimization 
difficult), 
high potential for link collisions at certain positions, and 
difficult computation of platform position from the actuator positions or 
forward kinematics. 
The new design has the following advantages: 
a reduced number of linkages between thin platform and base, and therefore 
fewer passive joints, resulting in less backlash and friction. 
less prone to collisions between linkages 
a larger workspace with fewer design parameters making geometric 
optimization easier 
both the forward and inverse kinematics can be calculated analytically, 
the addition of a single redundant actuator not only enhances the dynamic 
capabilities with little additional moving mass, but also reduces the 
number of singular positions. 
a limitless motion range in one of its angular degrees of freedom due to 
the serial actuator connected directly to the platform. 
the seventh acutuator can be eliminated a together, resulting in a 5-DOF 
device; this is not possible with the Triple Pantograph or the Stewart 
Platform. 
It is also possible to implement a tendon transmission system for the 
serial actuator to avoid carrying the mass of an actuator on the end 
effector. Alternatively, actuated extensible struts or auxiliary five-bar 
linkages could be used to give the platform a limited rotation, if this is 
called for by an application. (Note that this is distinguished from the 
Triple Pantograph by the use of actuated folding axes on the dual support 
structures, which give the device many of the advantages just listed.) 
Summary, Ramifications, and Scope 
Accordingly, it should be clear that the above geometrical constraints and 
description outline the concepts of a novel six degree of freedom 
manipulator having the following advantages over previous concepts: 
a reduced number of linkages between the platform and base, and therefore 
fewer passive joints, resulting in less backlash and friction. 
a larger workspace free of singularities and collisions between linkages. 
fewer design parameters making geometric optimization much more feasible. 
analytical solutions to both the forward and inverse kinematics. 
actuator redundancy that not only enhances the dynamic capabilities with 
little additional moving mass, but also increases the non-singular 
workspace. 
a limitless motion range in one of its angular degrees of freedom due to 
the serial actuator connected directly to the platform. 
The device could be used in any application where stiffness and precision 
are of utmost importance and a parallel platform type robot is preferred. 
It could be used as a master and/or slave robot in a teleoperation system. 
It could be used in virtual reality systems which incorporate robotic hand 
controllers or motion simulators. It can be used to create a force 
feedback input/output computer pointing device which has unlimited 
applications including human perception research, interactive 
computer-aided design interactive video games, interactive workspace 
managers and any other software application which can benefit from the 
incorporation of three dimensional translation/rotation tactile 
information exchange. Some or all of the actuators could be replaced with 
locking joints to create a multi-degree of freedom positioning table, or 
with passive joints to create a multi-degree of freedom position sensor. 
It can be used as an assembly robot or be made at a small scale for use as 
a six degree of freedom wrist for a serial robot. It could be made at a 
large scale for use in aircraft, car, trucking or other heavy-equipment 
simulators. 
Other actuator concepts beyond those illustrated are possible. For example, 
it is possible to remove the platform actuator altogether, when 
orientation of the platform is not necessary. Alternatively, one can 
implement a tendon transmission system for the platform actuator to avoid 
carrying the mass of an actuator on the end effector. By installing the 
platform motor on the base and setting pulley wheels into the wrist, elbow 
and shoulder joints of one of the five-bar linkages, the action of the 
platform motor can be communicated efficiently to the platform by the use 
of tendons. Auxiliary actuated linkages or extensible links could also be 
used to give limited tilt to the platform. 
Another variation on actuation of the alternative embodiments shown in 
FIGS. (5) to (7) can be created by substituting linear actuators for the 
waist assembly motors 112 and 132, and using a single rod in place of the 
linkages 114, 118, 134 and 138; the linear actuators would need to have 
rotatable supports. 
Accordingly, the scope of the invention should be determined not by the 
embodiments illustrated, but by the appended claims and their legal 
equivalents.