U.S. patent application number 12/692516 was filed with the patent office on 2010-09-30 for device for translating a force including a focused groove.
Invention is credited to Eugene F. Duval.
Application Number | 20100243377 12/692516 |
Document ID | / |
Family ID | 41819416 |
Filed Date | 2010-09-30 |
United States Patent
Application |
20100243377 |
Kind Code |
A1 |
Duval; Eugene F. |
September 30, 2010 |
DEVICE FOR TRANSLATING A FORCE INCLUDING A FOCUSED GROOVE
Abstract
A device to change the direction or point of application of a
force comprises a body having an axis, a groove formed within the
body so that the groove has a helical shape along at least a
portion of the axis, the groove adapted to receive a cable, wherein
a helical angle of the groove varies so that a tangent of the
helical angle along the groove substantially intersects a single
point remote from the body.
Inventors: |
Duval; Eugene F.; (Menlo
Park, CA) |
Correspondence
Address: |
FLIESLER MEYER LLP
650 CALIFORNIA STREET, 14TH FLOOR
SAN FRANCISCO
CA
94108
US
|
Family ID: |
41819416 |
Appl. No.: |
12/692516 |
Filed: |
January 22, 2010 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
10816616 |
Apr 2, 2004 |
7677540 |
|
|
12692516 |
|
|
|
|
60460771 |
Apr 4, 2003 |
|
|
|
Current U.S.
Class: |
185/37 ;
254/390 |
Current CPC
Class: |
F16H 19/0659 20130101;
F16M 2200/04 20130101; F16F 2230/0064 20130101; F16F 1/121
20130101; F16M 11/046 20130101 |
Class at
Publication: |
185/37 ;
254/390 |
International
Class: |
F03G 1/06 20060101
F03G001/06; F16H 55/36 20060101 F16H055/36 |
Claims
1. A device to change the direction or point of application of a
force, the device comprising: a body having an axis; a groove
formed within the body so that the groove has a helical shape about
at least a portion of the axis, the groove adapted to receive a
cable connectable with a target remote from the body; wherein a
helical angle of the groove varies so that when the groove receives
the cable, a tangent of the helical angle along the groove at a
point where the cable disassociates from the groove substantially
intersects the target.
2. The device of claim 1, wherein a first portion of the groove
includes a first helix shape and a second portion of the groove
includes second helix shape; wherein the cable is connectable with
a second target remote from the body; wherein a helical angle of
the first portion of the groove varies so that a tangent of the
helical angle along the first portion of the groove at a point
where the cable disassociates from the first portion of the groove
substantially intersects the first target; wherein a helical angle
of the second portion of the groove varies so that a tangent of the
helical angle along the second portion of the groove at a point
where the cable disassociates from the second portion of the groove
substantially intersects the second target.
3. The device of claim 1, wherein the groove is an output groove
adapted to receive an output cable; and further comprising: an
input groove formed within the body so that the input groove has a
helical shape along at least a portion of the axis, the input
groove adapted to receive an input cable connectable with a second
target remote from the body; wherein a helical angle of the input
groove varies so that a tangent of the helix angle along the input
groove at a point where the input cable disassociates from the
input groove substantially intersects the second target.
4. The device of claim 3, wherein a proximal end of the input cable
is fixedly associated with the body and a proximal end of the
output cable is fixedly associated with the body.
5. The device of claim 3, further comprising a pocket disposed
within the body; wherein a proximal end of one or both of the input
cable and the output cable includes a crimp receivable within the
pocket.
6. The device of claim 2, wherein the body is a pulley.
7. The device of claim 3, wherein the body is a capstan.
8. A device to change the direction or point of application of a
force, the device comprising: a body having an axis; an input
groove formed within a first portion of the body so that the input
groove has a helical shape about the axis, the input groove adapted
to receive an input cable; wherein a helical angle of the input
groove varies so that a tangent of the helical angle along the
input groove at a point where the input cable disassociates from
the groove substantially intersects a first target remote from the
body; and an output groove formed within a second portion of the
body so that the output groove has a helical shape along the axis,
the output groove adapted to receive an output cable; wherein a
helical angle of the output groove varies so that a tangent of the
helical angle along the output groove at a point where the input
cable disassociates from the groove substantially intersects a
second target remote from the body.
9. The device of claim 8, wherein the input groove is adapted to
receive an input cable and the output groove is adapted to receive
an output cable.
10. The device of claim 8, wherein a cable is received within the
input groove and the output groove.
11. The device of claim 8, wherein a proximal end of the input
cable is fixedly associated with the body and a proximal end of the
output cable is fixedly associated with the body.
12. The device of claim 9, further comprising a pocket disposed
within the body; wherein a proximal end of one or both of the input
cable and the output cable includes a crimp receivable within the
pocket.
13. The device of claim 8, wherein the body is a pulley.
14. The device of claim 8, wherein the body is a capstan.
15. A spring system having an adjustable spring constant,
comprising: an end plug including a helical groove in a face of the
end plug having a helix-angle that varies parabolically; a helical
extension spring; said end plug is adapted to be mated with the
helical extension spring so that the coil of the helical extension
spring is received in the helical groove; and a cable connected to
the end plug, wherein when the cable is placed in tension by a
load, the face of the end plug is urged against the coil of the
helical extension spring; wherein a counter force applied by the
helical extension spring in response to the load is adjustable by
repositioning the end plug along the helical extension spring.
16. The spring system of claim 15, wherein the helix-angle of the
helical groove decreases relative to a fixed location along the
coil and within the helical groove as one or both of the coil of
the helical extension spring and the end plug is adjusted to
increase the counter force applied by the helical extension
spring.
17. The spring system of claim 15, wherein: the helical groove is a
first helical groove and the face is a first face; and the end plug
further includes a second helical groove in a second face opposite
the first face, the second groove having a helix-angle that varies
parabolically; and when the end plug is mated with the helical
extension spring, the coil of the helical extension spring is
guided from the first helical groove to the second helical
groove.
18. The spring system of claim 17, wherein: the helix-angle of the
first helical groove decreases relative to a first fixed location
along the coil and within the first helical groove and the
helix-angle of the second helical groove increases relative to a
second fixed location along the coil and within the second helical
groove as one or both of the coil of the helical extension spring
and the end plug is adjusted to increase the counter force applied
by the helical extension spring.
19. The spring system of claim 15, wherein the cable is an input
cable, and wherein the spring system further comprises: a pulley
including an input groove and an output groove; the input cable
having a first end coupled to the input groove and a second end
connected with the end plug; an output cable having a first end
coupled to the output groove and a second end extending from the
first end; wherein the pulley is adapted to transfer a
counter-balance force to the second end of the output cable.
Description
CLAIM TO PRIORITY
[0001] This application is a continuation of U.S. patent
application Ser. No. 10/816,616, now U.S. Pat. No. 7,677,540, filed
Apr. 2, 2004, which claims benefit to U.S. Provisional Application
No. 60/460,771, filed Apr. 4, 2003, both of which are incorporated
herein by reference in their entirety.
FIELD OF THE INVENTION
[0002] This invention relates to mechanisms that convert the force
or torque from a spring into a constant force or torque.
BACKGROUND OF THE INVENTION
[0003] In the mid 1400's, conical shaped spiral pulleys called
fusees were first used to improve the accuracy of spring-powered
clocks. The fusee converted the linearly increasing torque from a
power spring into a constant torque. FIGS. 1a and 1b show two
different fusee mechanisms. In both figures, the clock spring is
located inside a drum on the left, and the conical fusee is located
on the right. A flexible chain connects the drum to the fusee. The
drum acts as a constant radius pulley and the fusee acts as a
variable radius pulley.
[0004] The fusee fell out of favor after the invention of constant
force and constant torque springs. The constant torque power
springs were no larger than the linear power springs that they
replaced. The fusee clocks were larger and they had more moving
parts. Constant force and constant torque springs haven't replaced
spiral pulleys for all applications. They store less energy per
pound and they have a shorter life than other springs. Their force
fluctuates slightly as they extend and retract. It's difficult to
produce constant force springs with a tight force tolerance. They
are not adjustable. In the United States, only a few dozen sizes of
constant force springs are available from stock. Other sizes must
be custom made.
[0005] In addition to the extra parts and space required, spiral
pulleys and fusees have other problems. The cables can rub and wear
on the sides of the grooves in the fusee. Rubbing occurs when the
cable is not tangent to the groove. For example, if the cable
approaches the fusee from a nearby idler pulley, the angle between
the cable and the groove can be large. This angular error is often
called the "fleet angle". U.S. Pat. No. 5,037,059 discusses one
specific solution to this problem.
[0006] Spiral pulleys and fusees are poorly understood and
difficult to design. The shape and size of a spiral pulley is
affected by many parameters. Most patents give only a limited
description of their geometry. For example, the 059 patent
describes the fusee as "corn shaped". U.S. Pat. No. 4,685,648
describes the spiral pulley as "irregular" or "snail-shaped".
[0007] FIG. 7 of the 648 patent shows a constant force mechanism
with two spiral pulleys. Both the input and the output pulleys are
spiral shaped. In other patents and references, only one of the two
pulleys has a spiral shape. In FIG. 5, only the input pulley is a
spiral. In FIG. 6, only the output pulley is a spiral. The 648
patent does not explain how to determine the shapes that will
produce a constant output force.
[0008] In FIGS. 2a, b, and c of this patent, prior art pulleys are
accurately drawn to show the shapes required to deliver a constant
force. In FIGS. 2a and 2c, the input pulleys have a spiral radius
as in FIG. 5 of the 648 patent. In FIG. 2b, the output pulley has a
spiral radius as in FIG. 6 of the 648 patent. For comparison, each
of the figures is drawn to the same scale. Each of the three
mechanisms is designed to deliver the same output force F.sub.out
and stroke L.sub.2.
[0009] In FIGS. 2a and 2b, the pulleys have been designed so that
the spring extension L.sub.1 is equal to the output stroke L.sub.2.
In FIG. 2c, the pulleys have been designed to minimize the size of
the mechanism. The spring extension in FIG. 2c is much smaller than
the output stroke. The resulting cable stress is much larger.
Compared to the FIGS. 2a and 2b mechanisms, the life and load of
the FIG. 2c mechanism is severely limited.
OBJECTS AND ADVANTAGES
[0010] It is an object of this invention to provide a pulley
mechanism for converting the force from a linear spring into a
constant force. The pulley mechanism should be significantly
smaller than previous constant force pulleys.
[0011] It is a further object that the mechanism should be accurate
and have low friction. If required, the mechanism should be
adjustable so that a desired force can be reached even with
commercial spring tolerances.
[0012] For general-purpose use, a limited number of pulley sizes
should cover a wide range of applications. The required output
force and travel may vary over a wide range. The orientation of the
spring relative to the output cable may vary. The pulley mechanism
should work with thousands of readily available helical extension
springs. The pulleys should be easy to apply and use. Cable
friction and wear caused by a nonzero fleet angle should be reduced
or eliminated.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] FIGS. 1a and 1b illustrate fusees in accordance with the
prior art.
[0014] FIGS. 2a-2c illustrate dual pulley, constant force
mechanisms in accordance with the prior art.
[0015] FIG. 3a illustrates an embodiment of a dual pulley, constant
force mechanism in accordance with the present invention.
[0016] FIG. 3b illustrates an alternative embodiment of a dual
pulley, constant force mechanism in accordance with the present
invention.
[0017] FIG. 3c illustrates a further embodiment of a dual pulley,
constant force mechanism in accordance with the present
invention.
[0018] FIG. 4 illustrates an embodiment of a dual pulley and spring
assembly including a differential spline hub in accordance with the
present invention.
[0019] FIG. 5 is an exploded view of the dual pulley assembly of
FIG. 4.
[0020] FIG. 6 is an exploded view of the spring assembly of FIG.
4.
[0021] FIG. 7 is a perspective view of an assortment of splined
pulleys.
[0022] FIG. 8 is an exploded view of an alternative embodiment of a
dual pulley assembly in accordance with the present invention.
[0023] FIG. 9 illustrates an embodiment of a dual helical pulley
and spring assembly in accordance with the present invention.
[0024] FIG. 10 is a perspective view of the dual helical pulley of
FIG. 9.
[0025] FIG. 11 is a side view of the dual helical pulley of FIG.
9.
[0026] FIG. 12 is a graph of the force deflection curve for a
typical extension spring.
[0027] FIG. 13 is a free body diagram of a pulley with a spring and
cable.
[0028] FIG. 14a is a graph of the input radius and input angle of
the pulley of FIG. 2a.
[0029] FIG. 14b is a graph of the output radius and output angle of
the pulley of FIG. 2b.
[0030] FIG. 15a is a graph of the input radius and input angle of
the dual pulley, constant force mechanism of FIG. 3b.
[0031] FIG. 15b is a graph of the output radius and output angle of
the dual pulley, constant force mechanism of FIG. 3b.
[0032] FIG. 16a is a graph of the input radius and input angle of
the dual pulley, constant force mechanism of FIG. 3a.
[0033] FIG. 16b is a graph of the output radius and output angle of
the dual pulley, constant force mechanism of FIG. 3a.
[0034] FIG. 17 is a graph of torque profiles including a parabolic
torque profile.
[0035] FIGS. 18a and 18b illustrate maximum angles of rotation for
two flat pulleys in which the groove lies in a plane.
[0036] FIG. 19a is a graph of corresponding tangent radius vs.
angle for the composite torque curves of FIG. 19b.
[0037] FIG. 19b is a graph of composite torque curves for an input
pulley.
[0038] FIG. 20a is a graph of corresponding tangent radius vs.
angle for the composite torque curves of FIG. 20b.
[0039] FIG. 20b is a graph of composite torque curves for an input
pulley.
[0040] FIG. 21a is a graph of corresponding tangent radius vs.
angle for the composite torque curves of FIG. 21b.
[0041] FIG. 21b is a graph of composite torque curves for an output
pulley.
[0042] FIG. 22 is a graph showing a sinusoidal transition for the
composite torque profile.
[0043] FIG. 23 is a graph showing the shape of a composite input
pulley with a center distance `m` as a parameter.
[0044] FIG. 24 is a graph showing the shape of a composite output
pulley with a center distance `m` as a parameter.
DESCRIPTION
Dual Pulley with Differential Spline Hub
[0045] FIG. 4 shows a typical embodiment of the dual pulley
constant force mechanism. FIG. 5 shows an exploded view of the dual
pulley assembly. FIG. 6 shows an exploded view of the spring
assembly.
[0046] The constant force mechanism has an input pulley 1 and an
output pulley 2. Each pulley has one flat face. The flat face of
one pulley rests against the face of the other. An 18 tooth
internally splined hole 3 passes perpendicularly through input
pulley 1. A 20 tooth internally splined hole 4 passes
perpendicularly through output pulley 2.
[0047] The input pulley is attached to the output pulley with a
differential spline hub 5. The hub is cylindrical. It has a round
bore through its center and one external annular groove at each
end. An 18 tooth external spline is located just inside the groove
at one end of the hub. A 20 tooth external spline is located just
inside the groove at the other end of the hub. The 18 tooth end of
the hub 5 engages the splined hole in the input pulley 1, and the
20 tooth end of the hub engages the splined hole in the output
pulley 2. The 18 tooth and 20 tooth combination provides for a
total of 180 evenly spaced orientations of the two pulleys.
[0048] The assembly is held together with a retaining ring 6 in
each hub groove. For low friction, a needle bearing 7 is pressed
into the bore in the hub 5. When cost is more important than
friction, the needle bearing can be eliminated, and the hub can act
as a bearing. The dual pulley assembly rotates about a shaft 8 that
passes through the bearing.
[0049] Both pulleys are non-circular. Each pulley has a v-groove 15
around its periphery. The shape or profile of the pulleys will be
covered later. Input cable 9 rides in the v-groove of the input
pulley 1. Output cable 10 rides in the v-groove of the output
pulley 2. The force in the output cable is constant over the
working range of the mechanism. A cable termination 11 is crimped
onto one end of each cable. Each cable termination is captured in a
slot 16 in the face of its pulley.
[0050] One end of a helical extension spring 12 is fixed to ground.
An adjustable end plug 13 is screwed into the spring coils at the
opposite or free end of the spring. A cable tension adjusting screw
14 is screwed into a threaded hole 20 in the center of the
adjustable end plug. The adjusting screw has an axial hole 36
through its center. The free end of the input cable 9 passes
through the hole in the adjusting screw. Another cable termination
(not shown) is crimped onto the free end of the input cable.
[0051] Looking at FIG. 6, a helical groove 17 is formed into both
faces of the end plug. The helix angle of the groove is not
constant. The helix angle varies parabolically from a small
helix-angle 18 at one end, to a large helix-angle 19 at the other
end of the groove.
[0052] FIG. 7 shows a perspective view of an assortment of splined
pulleys. There are four input pulleys on the left and four output
pulleys on the right. Any one of the input pulleys can be combined
with any one of the output pulleys to form a constant force
mechanism.
Dual Pulley with Radial Grooves
[0053] FIG. 8 shows an alternative construction for the dual pulley
assembly. The input pulley 21 has 36 wide radial grooves 23 on one
face. The output pulley 22 has 36 narrow radial grooves 24 on one
face. The two pulleys can be assembled face to face in any one of
36 evenly spaced orientations. Narrow grooves are used on the
output pulley and wide grooves on the input pulley so that it's
impossible to accidentally assemble two input pulleys or two output
pulleys. A cylindrical hub 25 has one external annular groove at
each end. As before, the assembly is held together with a retaining
ring 6 in each hub groove.
[0054] The radial groove design has several advantages. The hub is
smaller in diameter than the differential spline hub. Smaller
pulleys can be made with this construction. There are more grooves
and they engage each other at a greater radius compared to the
differential spline hub. The load carrying capability should be
improved. The radial groove design does not have as fine an angular
resolution as the differential spline hub.
Dual Helical Pulley
[0055] FIGS. 9, 10, and 11 show an alternative construction for the
pulleys. The dual helical pulley 26 is not flat as before. The
input v-groove 29 and the output v-groove 30 follow helical paths
as they wind around the pulley. The input and output grooves
intersect each other at their large diameter ends. This forms a
single continuous groove. A single cable 27 winds around the
groove. As before, a cable termination (not shown) attaches the
cable to the adjusting screw 14, end plug 13, extension spring 12
assembly. A cable crimp 28 is located a measured distance along the
cable. The crimp fits into a pocket 31 on the dual helical
pulley.
[0056] The path of the v-groove is not a true helix. The axial
advance of the groove is not constant with the rotation of the
pulley. The groove advances axially at a rate that keeps the
tangent to the groove aimed at a remote focal point 35. FIG. 11
shows how the tangent lines 33 and 34 intersect at the focal point.
The radial profile of the pulley v-grooves will be covered
next.
Pulley Profile
Introduction
[0057] The pulley shape or profile is a complex subject. The pulley
profile depends on several variables. For a given spring, output
force, and travel, there are an infinite number of profiles. Some
profiles are more useful than others are. One objective of the
preferred embodiment is to minimize the size of the pulleys.
[0058] The preferred pulley profile is a composite of shapes. The
output pulley has a constant radius portion, a sinusoidal radius
portion, and a linear radius portion. The input pulley has a
constant radius portion. It also has a portion where the radius is
determined by a sinusoidal portion of its torque profile and it has
a portion where its radius is determined by a linear portion of its
torque profile. FIGS. 3b and 3c show input and output pulleys with
composite profiles. For accurate comparison, the figures are drawn
to the same scale as the prior art in FIGS. 2a, b, and c. All
mechanisms in FIGS. 2 and 3 are designed to deliver the same output
force F.sub.out and stroke L.sub.2.
[0059] A better way to visualize pulley geometry is to look at a
Cartesian graph of pulley radius as a function of angle. FIG. 14a
shows a graph of the input pulley radius of the prior art spiral
pulley in FIG. 2a. FIG. 14b shows a graph of the output pulley
radius of the prior art spiral pulley in FIG. 2b. FIG. 15a shows a
graph of the radius of the composite profile input pulley shown in
FIG. 3b. FIG. 15b shows a graph of the radius of the composite
profile output pulley, shown in FIG. 3b.
There are three different types of radii. This can be confusing.
The true radius is the distance from the pulley axis of rotation to
a point on the pulley. The tangent radius is the normal distance
from the axis of rotation to a line that's tangent to the pulley.
The radius of curvature has its common definition. All three radii
are important. The size of the pulley depends on the true radius.
For example, the spiral pulley in FIG. 2a has a very large true
radius. The pulley torque is a function of the tangent radius. The
bending stress in the cable depends on the radius of curvature.
[0060] There are two important angles. The pulley angle measures
the pulley orientation relative to ground. The cable wrap angle
measures the cable orientation relative to the pulley. The two
angles are not the same because the orientation of the cable
relative to ground changes as the pulley radius changes. The pulley
shape is a function of the cable wrap angle. A graph of the pulley
radius as a function of the pulley angle does not fully define the
pulley shape.
[0061] It will be shown that it's useful to specify pulleys by
their torque profile, not their shape. Input pulleys have a
different shape than output pulleys. The pulley shape depends on
other variables. The constant force mechanism will work properly
only if the torque profile for the input pulley is symmetric to the
torque profile for the output pulley.
Pulley Radius Limitations
[0062] Not all of the spring energy can be converted to a constant
output force. In FIG. 2a for example, the radius of the spiral
pulley approaches infinity as the spring force approaches zero. An
infinite radius is obviously impractical.
[0063] In FIG. 2b, the radius of the spiral pulley approaches zero
as the spring force approaches zero. A very small radius is
difficult to control accurately. Any radius error will produce a
large force error. The pulley radius is also limited by the cable.
The stress in the cable gets large as the pulley radius gets
small.
Derivation of the Pulley Transfer Function
[0064] FIG. 12 is a graph of the force deflection curve for a
typical extension spring. The curve is linear at forces greater
than the initial tension F.sub.init. The spring constant K is the
slope of the curve. The linear portion of the curve can be
extrapolated back to zero force so that L is the spring
extension.
F=KL Eq. 1
[0065] Length L.sub.max is the theoretical distance, starting from
zero force, required to reach a maximum force, F.sub.max. E, is the
energy required to extend a theoretical spring starting at a force
of zero at zero extension, up to the maximum force F.sub.max. This
energy is equal to the total area under the curve.
E=1/2L.sub.maxF.sub.max
[0066] The fraction x, is a number between zero and one. The
constant force pulley mechanism operates between a force xF.sub.max
and F.sub.max. At the force xF.sub.max, the spring is extended by a
length x L.sub.max. The distance L.sub.1 is the operating spring
extension between force xF.sub.max and F.sub.max.
L.sub.max=xL.sub.max+L.sub.1
or L.sub.max=L.sub.1/(1-x)
[0067] E.sub.tran, is the energy transferred by the constant force
pulleys when the spring is extended over its operating range,
between x L.sub.max and L.sub.max.
E.sub.tran=F.sub.max(1+x)L.sub.1/2 Eq. 2
[0068] F.sub.out is the constant output force from the mechanism
and L.sub.2 is the output cable travel that corresponds to the
operating spring extension L.sub.1. If we assume that the pulley
mechanism is frictionless, then by conservation of energy:
E.sub.tran=F.sub.outL.sub.2 Eq. 3
Solving for F.sub.out:
[0069] F.sub.out=F.sub.max(1+x)L.sub.1/(2 L.sub.2)
The spring constant K can be calculated as follows:
K=(F.sub.max-xF.sub.max)/L.sub.1
Solving for F.sub.max, and substituting into the previous equation
yields:
F out = L 1 2 ( 1 + x ) K L 2 ( 1 - x ) 2 Eq . 4 ##EQU00001##
Equation 4 can be converted to the following form:
E tran = F out L 2 = L 1 2 ( 1 + x ) K ( 1 - x ) 2 Eq . 5
##EQU00002##
[0070] Note that equations 4 and 5 do not depend on the shape of
the pulleys. The equations hold for all six constant force
mechanisms in FIGS. 2 and 3.
Derivation of the Pulley Profile
[0071] FIG. 13 shows a free body diagram of a pulley with a spring
and cable. The pulley is mounted so that it's free to rotate about
an axis that is perpendicular to the page at point Q. The spring is
fixed in all three translational degrees of freedom at point R. The
spring is free to pivot or bend about an axis perpendicular to the
page at point R. Angle .lamda. is the pulley angle of rotation,
starting at .lamda.=0. The initial force in the spring is f.sub.0
where:
f.sub.0=xF.sub.max.
[0072] The cable travel is s, starting with s=0, and F=f.sub.0 at
.lamda.=0. The spring extension L.sub.1 is defined above. L.sub.1
is also equal to the total cable travel as the pulley rotates from
.lamda.=0 to .lamda..sub.max. We can call L.sub.1 the length of the
input pulley.
L.sub.1=s at .lamda..sub.max
The following parameters fully determine the shape of each pulley.
m=The center distance between points Q and R. .lamda..sub.max=The
maximum angle of pulley rotation. F(s)=The cable force on the
pulley. F is a function of s. .tau.(.lamda.)=The torque applied by
the mating pulley. .tau. is a function of .lamda.. For the input
pulley cable, the force is equal to the spring force:
F(s)=Ks+xF.sub.max=Ks+f.sub.0 Eq. 6
The torque .tau. on the input pulley produced by F is:
.tau. = Fr = ( Ks + f 0 ) r Eq . 7 Solving for r : r = .tau. ( Ks +
f 0 ) Eq . 8 ##EQU00003##
When the pulley rotates by an angle d.lamda., the resulting spring
extension will be:
ds=rd.lamda.,
This can be converted into a finite difference equation.
s n - s n - 1 = r n - 1 .DELTA..lamda. s n = r n - 1 .DELTA..lamda.
+ s n - 1 Eq . 9 ##EQU00004##
Now converting equation 8 into a finite difference equation:
r n = .tau. n ( Ks n + f 0 ) Eq . 10 ##EQU00005##
[0073] As seen in FIG. 13, when the pulley rotates by an angle
.lamda..sub.n, angle .phi. changes from .phi..sub.0 to .phi..sub.n.
As a result, the orientation of the cable relative to the pulley
changes by the cable wrap angle .omega., where:
.omega.=.lamda..sub.n+.phi..sub.n-.phi..sub.0
Looking at angle .phi.:
.phi.=sin.sup.-1(r/m)
Thus:
.omega..sub.n=.lamda..sub.n+sin.sup.-1(r.sub.n/m)-sin.sup.-1(r.sub-
.0/m) Eq. 11
The initial Conditions are:
.lamda. 0 = 0 .degree. ##EQU00006## .omega. 0 = 0 .degree.
##EQU00006.2## s 0 = 0. r 0 = .tau. 0 ( Ks 0 + f 0 ) = .tau. 0 f 0
##EQU00006.3##
[0074] If we know the constants K, f.sub.0, and m, and if we know
the pulley torque profile .tau.(.lamda.), then the pulley tangent
radius r can be calculated as follows. Starting with the initial
conditions above, using a small step size .DELTA..lamda., the shape
of the pulley can be solved numerically using equations 9, 10, and
11. The tangent radius as a function of the wrap angle gives us the
pulley shape.
[0075] When the cable is constrained to pass through the
perpendicular axis at point R, then the free body diagram in FIG.
13 is also valid for the output pulley. The same method can be used
to determine the shape of the output pulley. For the output pulley
cable, the cable force is constant and K=0.
F(s)=F.sub.out=f.sub.0
Prior Art Pulley Shape
[0076] FIGS. 2a, b, and c show examples of the prior art. In FIG.
2a, the output pulley has a constant radius. The torque between the
input and output pulley can be calculated. Similarly, in FIG. 2b,
the input pulley has a constant radius, and its torque profile can
be calculated.
[0077] In FIG. 2a, the output pulley has a constant radius of
r.sub.out, and the torque is constant at:
.tau..sub.a=F.sub.outr.sub.out
The equation for the torque between the pulleys in FIG. 2b can be
calculated as follows. The input pulley has a constant radius of
r.sub.in. Using equation 6 for the force on the cable, the input
pulley torque is:
.tau..sub.b=(Ks+xF.sub.max)r.sub.in
[0078] The output force F.sub.out and stroke L.sub.2 are determined
by application requirements. If we make assumptions about any two
of the three variables L.sub.1, x, and K, we can solve for the
third variable using equation 5. The center distance m can be
selected to suit the geometric constraints of the application. We
now have enough information to determine the shape of the pulleys
for the prior art mechanisms in FIGS. 2a, 2b, and 2c.
Minimizing the Size of the Dual Pulley Mechanism
[0079] Many parameters affect the size of the dual pulley
mechanism. These include the input pulley length L.sub.1, the
output pulley length L.sub.2, the output force F, the spring
constant K, the fraction of unused spring extension x, and the
torque profile .tau.(.lamda.) and .lamda..sub.max. The center
distances m.sub.1 and m.sub.2 affect the shape of the pulleys, but
they have relatively little affect on the maximum size.
[0080] To make the problem easier, we can assume that several
parameters are fixed. We can assume that we have a given task that
requires a force F.sub.out over an extension L.sub.2. We can also
assume a value for x. All of the pulley mechanisms have similar
problems if we try to make x too small. Finally, we can assume that
L.sub.1=L.sub.2.
[0081] The last assumption isn't always valid, but it's useful for
the following reason. Mathematically, it's always possible to
decrease the size of the input pulley L.sub.1, by using a spring
with a higher stiffness K. The higher stiffness and smaller input
pulley will increase the load on the input cable. When
L.sub.1=L.sub.2, the maximum cable force F.sub.in is limited to
F.sub.in<2F.sub.out. When the size of the input pulley is
reduced by decreasing L.sub.1, the input cable force F.sub.in can
grow much larger than 2F.sub.out. Setting L.sub.1 equal to L.sub.2
puts a limit on the maximum cable load.
Pulley Torque Profile
[0082] FIGS. 2a, b, c and 3a, b, c show six different constant
force mechanisms. Each mechanism has been designed to deliver the
same output force and stroke. For comparison, all figures have been
drawn to the same scale. FIGS. 2a, b, and c are prior art. FIGS.
3a, b, and c are new. FIGS. 14, 15, and 16 show graphs of the
pulley radius for most of the examples.
[0083] The torque is a constant for the mechanisms in FIGS. 2a and
2c. The mechanism in FIG. 2b has a linearly increasing torque
profile.
[0084] The mechanism in FIG. 3a has a parabolic torque profile. The
mechanisms in FIGS. 3b and 3c have composite torque profiles. The
input cable travel is equal to the output cable travel or
(L.sub.1=L.sub.2) for all but FIGS. 2c and 3c.
[0085] FIG. 17 shows the torque profiles for all but the last
mechanism. The same amount of energy is transferred by each
mechanism. As a result, the area under each torque curve is the
same. The pulley diameter can be minimized by maximizing the pulley
angle of rotation. For a given type of torque profile, the pulley
diameter is inversely related to the maximum angle of rotation.
Limit on the Maximum Angle of Rotation
[0086] For a flat pulley in which the groove lies in a plane, there
is a limit on the angle of rotation. FIGS. 18a and 18b show two
shapes for an input pulley with a constant torque profile. In FIG.
18a, the shape is calculated assuming the pulley will rotate to a
maximum angle .lamda..sub.max=230.degree.. In FIG. 18b, the shape
is calculated assuming the maximum angle is
.lamda..sub.max=300.degree..
[0087] In FIG. 18b, the pulley collides with the cable well before
reaching its 300.degree. design limit. For flat pulleys, the shape
shown in FIG. 18b is unacceptable. FIG. 18a shows that
.lamda..sub.max is limited to a little more than 230.degree. for
the constant torque profile mechanism in FIG. 2a. The maximum angle
of rotation is not the same for all torque profiles. The maximum
angle may also depend on the center distance m, and the unused
fraction of the spring extension x.
The Composite Profile Pulley
[0088] FIG. 19b is a graph of several composite torque curves. The
bottom torque curve is shown with a heavy line. FIG. 19a is a graph
of the corresponding input pulley radius for each of the torque
curves. The lower pulley radius curve with the heavy line
corresponds to the torque curve with the heavy line.
[0089] Only one of the input pulley curves has a constant radius
segment. The input pulley will have a constant radius only if the
torque curve is linear, and the slope and intercept of the line are
properly matched. A torque curve that corresponds to a constant
pulley radius can be found in the following way. Select a value for
the desired torque at a zero pulley angle. This is the intercept.
Then take a guess at the slope of the torque versus pulley angle
line, and numerically solve for the pulley shape. If the radius is
not constant, modify the slope and recalculate the pulley shape.
This process can be used to iteratively solve for the slope of the
torque curve that yields a constant pulley radius.
[0090] FIGS. 20a and 20b are graphs for an input pulley. The graph
in FIG. 20b shows several composite torque curves. The graph in
FIG. 20a shows the corresponding pulley radius curves. Using the
above process, each torque curve has been selected so that the
corresponding pulley radius curve is constant over part of its
rotation.
[0091] The area under each of the torque curves in FIG. 20b is
identical. As a result, each torque curve represents the same
amount of energy. The energy is equal to the constant output force
multiplied by the output cable travel L.sub.2. Each composite curve
has a linearly increasing portion and a constant portion. Each
curve changes from linear to constant at a specific angle
.lamda..sub.b. The values of .lamda..sub.b yielding the desired
energy can be solved for iteratively.
[0092] FIGS. 21a and 21b are graphs for an output pulley. Output
pulley torque curves are shown in FIG. 21b. Note that the curves in
FIGS. 20b and 21b are mirror images of each other. When the input
pulley is at the start of its travel, or
.lamda..sub.input=0.degree., the output pulley is at the end of its
travel or .lamda..sub.output=300.degree.. The torque curves are
identical. They look reversed because they are shown relative to
different coordinate systems.
[0093] FIG. 21a shows radius curves for the output pulley. These
curves correspond to the torque curves in FIG. 21b. Each of the
curves has a constant radius segment. Note that the constant radius
portion of each curve corresponds to the constant portion of the
torque curve. The constant radius portions of the input and output
pulleys correspond to different parts of the torque curve.
[0094] With equal energy torque curves, when the maximum diameter
of the input pulley decreases, the maximum diameter of the output
pulley increases. As a result, the size of this dual pulley
mechanism will be minimized when both the input pulley and the
output pulley have the same constant diameter. This occurs
approximately when .lamda..sub.b.apprxeq.133.degree. for the input
pulley torque profile. Remember that we have also assumed that
L.sub.1=L.sub.2.
[0095] If we relax the earlier assumption that L.sub.1=L.sub.2,
then the size of the dual pulley can be reduced further. Decreasing
.lamda..sub.b for the input pulley, decreases the diameter of the
output pulley and increases the diameter of the input pulley. But
if we let L.sub.1<L.sub.2, then the input pulley diameter can be
reduced too. Solving iteratively with smaller values of
.lamda..sub.b we find that the maximum allowable pulley angle
.lamda..sub.max increases to .lamda..sub.max=302.degree. at
.lamda..sub.b.apprxeq.80.degree.. At values of .lamda..sub.b below
80.degree., the maximum allowable pulley angle .lamda..sub.max
starts to decrease again.
Eventually, the decreasing .lamda..sub.max will offset the effect
of decreasing .lamda..sub.b, and the pulley diameter will start
getting larger again.
[0096] FIG. 3c shows the input and output pulleys with a composite
torque profile and .lamda..sub.b.apprxeq.80.degree.. The mechanism
in FIG. 3c has the same output force F and extension L.sub.2 as the
previous five examples. The spring extension L.sub.1 has been
decreased by a factor of about 0.83. From equation 5, this will
increase the input cable force by the reciprocal of 0.83 or by a
factor of 1.20
[0097] In the limit, by decreasing .lamda..sub.b to zero,
.lamda..sub.max decreases to a little over 130.degree., just as in
FIG. 2a. We end up with the mechanism shown in FIG. 2c. Compared to
FIG. 2a, the input pulley size L.sub.1 is reduced by a factor of
0.28 Using equation 5, in FIG. 2c, the input cable force will
increase by a factor of 3.5.
[0098] The mechanism in FIG. 3c is smaller and it has lower cable
forces than the prior art mechanism in FIG. 2c.
Transition Between Segments of the Composite Torque Profile
[0099] An assumption was made in the previous section. The
composite torque profiles are shown with sharp transitions between
the linear and the constant segments. The torque profile can't make
a sharp transition.
[0100] When a constant radius portion of a pulley makes a sharp
transition to a decreasing radius, the torque profile follows a
sinusoidal curve. Assuming a constant radius r and cable force F,
the torque profile follows equation 12.
.tau.=Fr sin(.lamda.) Eq. 12
[0101] In other words, even if the radius drops sharply from r to a
smaller radius, the torque is a function of the radius to the
tangent, which is r sin(.lamda.). FIG. 17 shows a composite torque
profile with the sharpest sinusoidal transition between the
segments. Note that the difference in area between the sharp
transition and the sinusoidal transition represents only about 0.1%
of the total area under the torque curve. As a result, the previous
optimization is still valid.
[0102] When the torque profile has the sharpest sinusoidal
transition between its segments, the pulley has a sharp corner.
This is usually unacceptable.
[0103] The radius of curvature of the sharp corner is zero. This
will overstress and rapidly fatigue a cable. The sharp corner in
the pulley profile can be rounded off in a variety of ways.
Arbitrarily rounding the corners of both pulleys will produce
errors in the output force. The desired output force can be
maintained by further rounding the torque profile and then
calculating the input and output pulley profiles from the new
torque profile.
[0104] A simple way to round the torque profile is to use a
sinusoidal transition with a smaller magnitude than before.
Equation 13 describes a new transition portion for the torque
curve. .tau..sub.const is the constant portion of the torque
profile and .tau..sub.linear is the linear portion of the torque
profile. The new transition portion covers a full 90.degree. of
pulley rotation, from .lamda.=.lamda..sub.1 to
.lamda.=(.lamda..sub.1+90.degree..
.tau..sub.tran=(Fr-S)+S sin(.lamda.-.lamda..sub.1) Eq. 13
Where
[0105] .tau..sub.const=Fr [0106] .tau..sub.linear=S.lamda.+b [0107]
.lamda..sub.1=(Fr-S-b)/S [0108] S=The slope of the linear portion
[0109] b=The intercept for the linear portion
[0110] A graph of equation 13 is shown in FIG. 22. Note that the
sinusoidal curve is tangent to both the linear and the constant
portions of the original composite curve. The large radius
transition decreases the area under the torque curve or the energy
transferred by less than 0.4%.
Other Pulley Profiles
[0111] There are infinite pulley shapes that will produce a
constant output force. Factors other than minimum size may be more
important for some applications. For example, the life and strength
of the cable is affected by the minimum bend radius of the pulleys.
Alternatively, for another application, the sensitivity to cable
angular alignment may be more important.
[0112] FIG. 17 shows an example of a parabolic torque profile. The
peak torque .tau..sub.max occurs at the maximum pulley angle
.lamda..sub.max. The minimum torque .tau..sub.min occurs at
.lamda.=0. Finally, the minimum torque
.tau..sub.min=0.4569.tau..sub.max. FIG. 3a shows a dual pulley
mechanism with the given parabolic torque profile. For comparison,
the mechanism is designed to deliver the same output force
F.sub.out and stroke L.sub.2 as the other mechanisms in FIGS. 2 and
3. FIG. 16a shows a plot of the input pulley radius and FIG. 16b
shows a plot of the output pulley radius.
[0113] Note that the parabolic profile dual pulley mechanism is
about 11% larger than the equivalent composite profile mechanism in
FIG. 3b. The parabolic mechanism is about 25% smaller than the
smallest equivalent prior art in FIG. 2b. There are infinite pulley
shapes between the minimum sized composite profile and the prior
art. Coefficients can be determined for a torque profile consisting
of any higher order polynomial.
The Affect of the Center Distance on the Pulley Profile
[0114] The center distances m.sub.1 and m.sub.2 affect the shape of
the pulleys. This occurs because the center distance affects the
cable wrap angle. When the center distance is large, the pulley
angle is the same as the cable wrap angle. The difference between
the two angles increases when the center distance gets small. FIG.
23 shows the shape of an input pulley with a composite torque
profile. The pulley shape is shown for a variety of center
distances m.sub.1. FIG. 24 shows the shape of an output pulley with
a composite torque profile. The output pulley shape is shown for a
variety of center distances m.sub.2.
Standardization of the Pulleys
[0115] Input and output pulleys with symmetric torque profiles over
a given range of pulley angle will produce a constant output force.
The pulleys will behave according to equation 5.
E tran = F out L 2 = L 1 2 ( 1 + x ) K ( 1 - x ) 2 Eq . 5
##EQU00007##
[0116] Two input pulleys may have identical torque profiles but
different shapes. Both the center distance m.sub.1 and the fraction
x affect the shape of the input pulley. Center distance m.sub.1 and
the fraction x have no affect on the shape of the output pulley.
Two output pulleys may have identical torque profiles but different
shapes. The center distance m.sub.2 affects the shape of the output
pulley, but not the shape of the input pulley.
[0117] A series of sizes of input and output pulleys can be
designed with symmetric torque profiles. The same value of x can be
used for all input pulleys in the series. With x=0.3 the size of
the pulleys is reasonable and most of the spring energy storage
capacity is used. Each input pulley size L.sub.1 can have a
standard center distance m.sub.1. Each output pulley size L.sub.2
can have a standard center distance m.sub.2. A good choice for the
standard center distance will allow a pulley to be used over a wide
range with little error. For example, assume that an output pulley
with L.sub.2=160 mm (6.30 inches) has a design center distance of
m.sub.2=12 inches. Looking at FIG. 24, there is little change in
the pulley profile over the range of 8 in.<m.sub.2<.infin..
For many applications, the pulley would work well over that range.
For highest accuracy, the pulley should be used at its design
center distance.
Pulley Alignment and Coupling
[0118] To function properly, the pulleys must be aligned relative
to each other. Input and output pulleys must be connected by a
torsionally rigid coupling. The profile of each pulley is generated
relative to a line through point Q and point R as shown in FIG. 13.
Phase angle .theta. is the angle between input pulley line QR and
output pulley line QR.
[0119] For general purpose use, the ability to adjust .theta. is
desirable. This allows the spring and cable to be located where
they fit best for any application. There are many ways to connect
and align the pulleys. As mentioned earlier, the preferred method
with the differential spline hub is shown in FIGS. 4 and 5. FIG. 8
shows an alternative construction with radial grooves in one face
of each pulley. There are many other ways of constructing an
adjustable dual pulley mechanism. The two pulleys can be screwed
together, with a bolt pattern evenly spaced in a circle. The dual
pulleys can be manufactured in one piece. They can be welded or
glued together. The pulleys can be press fit or staked onto the
hub.
Adjustable Force End Plug
[0120] The output force from the dual pulley mechanism can be
adjusted by changing the spring constant. Equation 4 shows that the
output force F.sub.out is proportional to the spring constant K.
Unfortunately, it's difficult to manufacture springs with a close
tolerance on K. The tolerance on K for helical extension springs is
typically no better than .+-.5.%.
[0121] FIG. 6 shows the threaded plug mechanism for adjusting the
spring constant of the helical extension spring. The mechanism
consists of a threaded plug that screws into either end of the
spring. The plug has one turn of a custom screw thread. The load is
applied to the spring through the end plug, rather than the through
the typical end hook.
[0122] The compliance of a helical extension spring is proportional
to the number of active coils. The spring constant K is equal to
the reciprocal of its compliance. The number of active coils N can
be adjusted by screwing the end plug into or out of the spring.
This enables the plug to make a very fine adjustment of the output
force. A tight tolerance on the spring constant is not needed.
[0123] The end plug has other benefits. It's significantly shorter
than the usual end hooks. To save space, an end plug can be used at
both ends of the spring. If properly designed, the end plug can
reduce the maximum stress in the spring. The highest stress in an
extension spring is usually located in the end hooks. With the
lower stress, the spring will have a longer life. A plug mounted in
the fixed end of the spring can be rigidly fixed to ground. For
some applications, an internal thread geometry may fit better than
the plug's external thread.
[0124] The thread pitch is not constant. The pitch starts at a low
rate and it increases parabolicly over the single turn. The
parabolic pitch is the same on both faces of the single thread.
This results in a thread that is thin at both ends and thick in the
middle. The spring coil that contacts the outside face of the
thread follows the same parabolic pitch. As a result, the load from
the coil is evenly distributed over the single turn. This
eliminates the bending loads and stress produced by spring end
hooks.
Helical Pulleys or Fusees
[0125] As shown earlier, when the pulley groove is constrained to a
plane, the pulley rotation is limited to .lamda..sub.max. The
rotation limit can be avoided if the pulley groove advances axially
as the pulley rotates.
[0126] A helix is commonly defined as a curve that lies on the
surface of a cylinder or cone and cuts the element at a constant
angle. The path of the groove of a constant force pulley would not
fit this definition. The path may not lie on a cone, and the helix
angle may not be constant. Helical will be used to differentiate
these pulleys from flat pulleys.
[0127] For helical constant force pulleys, the radius to the groove
can be calculated as it was for flat pulleys. Without the
limitation on .lamda..sub.max, the radius to the groove and the
pulley diameter can be much smaller. The radius to the groove
scales as 1/.lamda..sub.max.
[0128] One problem that arises with a helical pulley is that the
cable can rub on the sides of the groove. For pulleys and capstans,
the term "fleet angle", is defined as the angle between the cable
and the tangent to the pulley groove. To limit friction and wear,
it's desirable to keep the fleet angle small. This is not always
possible, especially with short center distances m.sub.1 or
m.sub.2.
[0129] The easiest way of designing the helical groove is to
linearly advance the groove in an axial direction as the pulley
rotates. This will produce a constant pitch groove. Alternately,
the groove can be constructed with a constant helix angle. Both of
these methods have fleet angle problems.
[0130] A preferred solution is to advance the groove axially at a
rate that aims or focuses the tangent to the groove at a single
remote point. The groove will start with a large helix angle at the
large radius end of the helical pulley. The helix angle will
decrease continuously to a small value at the small end of the
pulley. A pulley with this type of "focused" groove is shown in
FIGS. 9, 10, and 11. A fleet angle of zero can be maintained over
many pulley revolutions. Ideally, the focus point should be located
at the center distance m that is used to calculate the pulley
radius profile. The figures show how input and output helical
pulleys can be combined into a single structure. The grooves
intersect each other at the large diameter ends of the pulleys.
Depending on the required phase angle between the input and output
pulleys, a transition groove may be needed between the two pulley
grooves.
[0131] The single groove design eliminates one cable and two cable
terminations. The loads and stresses produced by the cable
terminations are eliminated. With the lower stress, the pulleys can
be constructed from lower strength materials including plastics.
The plastic may be of a type suitable for bearings. This will
eliminate the need for separate bearings. The pulleys can rotate
directly on a shaft.
[0132] For a single cable mechanism, if the tension ratio between
the input and the output falls within the following range, the
cable will not slip on the pulley.
e.sup.-.mu..theta.<F.sub.in/F.sub.out<e.sup..mu..theta.
[0133] Where .mu. is the coefficient of friction between the pulley
and the cable, and .theta. is the total wrap angle in radians, of
the cable on the pulley. Friction will transfer the entire load
between the cable and the pulley. A variety of other methods can be
used to keep the cable from slipping. These include using a crimp,
a knot, or a bead tied onto the cable. The crimp, knot, or bead can
be retained by a slot that crosses the pulley groove. The cable can
be jammed into a narrow or serrated slot in line with the pulley
groove. Alternatively, the cable can be glued or welded in
place.
[0134] A helical single groove dual pulley may have two or more
parts that can be phased relative to each other as previously
described.
Other Options
[0135] Dual pulleys can be designed to deliver output force
profiles that are not constant. Pulleys can also be designed to
accept other spring force profiles.
[0136] In this disclosure, the input and output pulleys are rigidly
coupled. The pulleys can also be designed to work on two different
axes similar to the prior art in FIGS. 1a and 1b.
[0137] The differential spline hub will work with other numbers of
splines on each end.
[0138] The pulley v-grooves can be eliminated for some
applications. For example, a flat strap can be used on a flat
pulley surface. Chains can be used with toothed pulleys.
Advantages of the Composite Torque Profile, Dual Pulley, Constant
Force Mechanism
Smaller, Lighter, Less Inertia, Longer Cable Life, Higher Load, and
Better Balance
[0139] The composite torque profile minimizes the size of the
pulleys. With smaller pulleys, less space is required, the pulleys
are lighter, and they have much less rotational inertia.
[0140] Cable life and load can also be improved. Pulley size, cable
life, and operating load are all related. The cable life is
improved by increasing its bend radius and by decreasing the cable
load. The bend radius is equal to the radius of curvature of the
pulley, not the pulley radius. For a given pulley size, the
composite torque profile maximizes the pulley radius of curvature.
For a given pulley size, the composite profile also maximizes the
input cable travel L.sub.1. This reduces the spring and cable
force. The lower force and the larger radius of curvature increase
the cable life.
[0141] The composite torque profile pulleys are easier to balance.
Compared to previous spiral pulleys, their center of gravity is
closer to the axis of rotation. This makes it easier to balance the
pulleys for greater force accuracy and less vibration.
Modular, Standardized, Low Cost, and Easy to Use
[0142] A small number of standardized input and output pulleys with
symmetric torque profiles can be used to cover a wide range of
constant force applications, from low force to high force and from
short stroke to long stroke. Pairs of input and output pulleys can
be used in combination with thousands of available extension
springs. For a given output force and stroke, the spring can be
selected for the required cycle life. Within limits, the spring
length and outside diameter can be selected to fit the available
space. Selecting appropriate input and output pulleys is a simple
process. For most applications, a custom design isn't needed. The
small number of pulley sizes needed to cover a wide range of
applications should make it feasible to mass produce the pulleys at
low cost.
[0143] The differential spline hub gives the freedom to orient the
spring and the output cable where they fit best. With the hub, the
pulleys can be rapidly and accurately assembled with high angular
resolution.
Better Accuracy
[0144] A dual pulley mechanism can deliver an output force more
accurately than a constant force spring. The force from a constant
force spring fluctuates due to local geometric variations along the
spring. Local variations along the length of a helical spring do
not produce the same force variations.
[0145] The force error of a pulley mechanism is a linear function
of the pulley profile. For example, if the pulley radius is 10%
larger than it should be, the resulting force error will be 10%.
The force error for a constant force spring is a cubic function of
the spring thickness. A 10% thickness error will produce a force
error of about 33%.
[0146] If a specific force is required from a dual pulley
mechanism, an end plug can be used to adjust the helical spring.
The output force can be adjusted to within a fraction of one
percent. An expensive tight tolerance spring is not required. The
tolerance for a constant force spring is typically about + or
-10%.
Lighter Weight and Longer Life Spring
[0147] Helical extension springs are ideal for the dual pulley
constant force mechanism. When operated at similar stress levels,
helical springs can store approximately twice as much energy per
pound compared to constant force springs. Constant force springs
typically have a relatively low cycle life between 4,000 and 40,000
cycles. Helical springs can be designed for a much longer life.
Fusee Advantages:
Smaller Size, Fewer Parts, Less Wear and Friction, and Less
Sensitive to Alignment Errors
[0148] The outside diameter of the spiral pulley can be reduced by
increasing the total rotation of the pulley. A multiturn spiral
pulley is called a fusee. The fusee diameter can be much smaller
than an equivalent flat spiral pulley. The fusee will be wider than
the flat pulley.
[0149] A fusee is less sensitive to angle errors and to errors in
the center distance m. With a larger total angle of rotation, the
fusee radius changes more slowly. As a result, the fusee is less
sensitive to angular alignment errors. When a cable wraps onto a
variable radius pulley, the cable direction changes. The direction
change is a function of both the center distance m and the total
radius change of the pulley. A fusee with a greater total rotation
will have a smaller radius change than an equivalent flat pulley.
As a result, the fusee is less sensitive to center distance
errors.
[0150] The focused groove aims the fusee groove at a remote point.
This reduces the cable friction and wear.
[0151] The input and output grooves can be combined into one
continuous groove. Only one cable is needed for the mechanism. With
only one cable, the cable terminations can be eliminated. The
stress produced by the cable terminations is eliminated too. With
lower stress, the fusee can be made from a less expensive material.
The fusee can be molded out of plastic. With a suitable plastic,
the fusee can rotate directly on the shaft. Additional bearings
aren't needed.
[0152] The fusee can be made in one piece. It can also be made in
two or more parts, with the input pulley in one part and the output
pulley in another part. A spline mechanism can be used to adjust
and align the parts.
* * * * *