Riverhawk Company
215 Clinton Road
New Hartford NY(315)768-4937®

Free-Flex
Flexural Pivot
Engineering DataPREFACE
Patented Flexural Pivot
A unique bearing concept for applications with limited angular travel
RIVERHAWK produces the patented FREE-FLEX® flexural pivot for aerospace,commercial and industrial bearing applications involving limited angular travel. As analternative to rolling element bearings and other devices providing rotational support forlimited angular rotation, the FREE-FLEX® pivot offers superior operating
characteristics. It has demonstrated performance and installed cost advantages overconventional bearings in many applications.
The FREE-FLEX® pivot is a frictionless, stiction-free bearing ideally suited for angulardeflection (rotation) of up to 60°. It is a simply packaged, compact, easily installed
bearing with high radial stiffness (up to 100,000 lb/in), no backlash, no metal-to-metal
contact and having predictable and repeatable performance. The pivot is ideal for
precise positioning: adjustments in 0.00005-inch increments can be made with no lostmotion. The unique combination of performance characteristics found only inRIVERHAWK FREE-FLEX® pivots is often the enabling technology which makes acomponent or subsystem design approach practical.
The FREE-FLEX® pivot consists of flat springs crossed at 90° and, supporting
cylindrical counter-rotating sleeves, as shown in Figures 1 and 2. Friction, stiction (theforce required to cause one body in contact with another to move), fretting corrosion,
lubrication, "space welding" and lubricant out-gassing in space vacuum applications
are all avoided in the RIVERHAWK FREE-FLEX® pivot because there is no metal-tometal contact.
By matching pivot size and spring rate to the application, cyclic stress on the springs
may be maintained at a low enough value to assure infinite cyclic life. To demonstrate
this life, a FREE-FLEX® pivot was cycled for over 12 billion cycles over a period oftwenty years, outliving several of the machines used to test it.

Page 1

The FREE-FLEX® pivot is available in two basic mounting configurations: cantilevered
to support an overhung load; and double-ended to bridge-support a central load. Stockoutside diameter sizes are from .125 in to 1.0 in, withstanding radial loads to 1600 lb inboth series. Standard sizes in several torsional spring rates are available off the shelfin both cantilevered (Series 5000) and double-ended (Series 6000) designs to matchuser load and mounting requirements. The materials nominally used for standard
pivots are AISI 410 or 420 corrosion-resistant steel for the bodies, and AISI 420
corrosion-resistant steel for the flat spring flexures. Normal assembly is by brazing thesprings to the body halves.
For application-specific requirements such as elevated ambient temperature thesprings are electron beam welded to the body. Special spring materials include
Inconel, beryllium copper and titanium. Special configurations are available uponrequest.
Covered by U.S. Patents: 3,807,029; 3,811,665; 3,813,089; 3,825,992; 4,327,527, and by foreign patents.

Page 2

RIVERHAWK FREE-FLEX® FLEXURAL PIVOT
Design Considerations
MAJOR PERFORMANCE CHARACTERISTICS••••••••••••••HIGH RADIAL STIFFNESSHIGH AXIAL STIFFNESSFRICTIONLESSSTICTION-FREE
NOT SUSCEPTIBLE TO FALSE BRINELLING
LOW HYSTERESISLOW CENTERSHIFTEXCEPTIONAL REPEATABILITY
PREDICTABLE PERFORMANCELUBRICATION NOT REQUIREDMAINTENANCE NOT REQUIREDELECTRICAL CONTINUITY
INFINITE CYCLE LIFE (SEE LIFE CURVES)AMBIENT TEMPERATURE RANGE OF -400°F to +1200°F

ADDITIONAL CHARACTERISTICS•••••••RADIATION RESISTANCELOW THERMAL DRIFTNO RUBBING SURFACESCONTAMINANT TOLERANTOPERATES IN VACUUM OF SPACESELF-CENTERINGRELIABLESUMMARY STATEMENTTHE FREE-FLEX® FLEXURAL PIVOT IS AN ELEGANTLY SIMPLE BEARING
WHICH PROVIDES PRECISE SINGLE-PLANE POSITIONING AND FRICTIONLESSMOTION OF LIMITED ANGULAR ROTATION DEVICES.

Page 3

GLOSSARY OF FLEXURAL PIVOT TERMS
Axial Load

This load is also called "Thrust Load”. This Load acts in direction oflongitudinal axis of Pivot

Axial Rate

The number of pounds of axial (thrust) load necessary to create a
specific unit of relative motion between the flexure-connected
portions of the pivot in the longitudinal direction. It is usually statedas pounds per inch. For example, an axial load of 50 pounds isfound to create a motion of 0.001 inches; the axial rate is 50 divided
by 0.001 inches or 50,000 pounds per inch.

Center Shift

The difference between the diameter centers of the moved portion of
the pivot and the portion (or portions) that are fixed. Basic center
shift is a kinematic characteristic that occurs in more or less degree
as a function of the angle deflected; it occurs the full length of theshifted diameter.
An auxiliary center shift is mechanical and is caused by radial load(see "Radial Rate"). Shift of the full length of the diameter does nottheoretically take place, but for practical purposes, within the pivot
standard dimensions; it is considered as taking place the full length ofthe pivot diameter.

Compression (Vc) A radial load directed to the pivot such that the highest flexure stressis compression.

Cycle

One cycle is the sum of angular motion from the null position to aparticular angle, the return to the null position, the angular motion
from the same angle in the opposite direction and the return to null.

H LoadA radial load directed such that it bisects the crossed flexures and isparallel to the travel slots.

Horizontal Load A radial load perpendicular to "V load"; see "H Load" and "V Load".
Hysteresis

The total amount of variation from null position when a torque isapplied such as to produce a complete cycle. It is expressed inminutes or seconds, as applicable.

K"K" is a designation for "Torsional Rate" used in the torsional rateequation.

Page 4

Linearity

The degree which a plot of torque (about the longitudinal axis) vs.
deflection is a straight line.

MomentA torque applied in a given plane through a pivot other than aroundthe longitudinal axis. RIVERHAWK Engineering usually considers it
as a torque in addition to that caused by an offset V, H or T load.

Moment (Total)

The total torque applied in a given plane through a pivot other thanaround the longitudinal axis. It is the algebraic sum of moments
caused by radial and thrust loads and any additional from othersources.

Moment-Turning The amount of torque necessary to rotate the pivot a specific angle.
This term, although related to "Torsional Rate", is not identical to"Torsional Rate".
Non-Linearity

The degree which a plot of torque (about the longitudinal axis) vs.
deflection varies from a straight line; it is the opposite of linearity.

Null Position

The position of zero angular travel when the pivot is under no load,with no applied torque about any axis and at a specific temperature.

Null Shift

The change in the null position due to effects other than applied
loads and/or torques. This term is not to be confused with hysteresis.

P LoadA radial load directed such that it is directed exactly in line with apivot flexure.

Radial Load

A load directed to the pivot center from any angle around the pivot
circumference.

Radial Rate

The number of pounds of radial load necessary to deflect the pivotstructures (as measured at the outer diameter) a specific unit ofmeasure. It is usually stated as pounds per inch. For example, aradial load of 10 pounds is found to deflect the pivot 0.0001 inches;
the radial rate is 10 divided by 0.0001 inch or 100,000 pounds perinch.

RadianThere are 2PI radians in every 360o (circle), thus one radian is57.2956 + degrees. In general, the value of 57.3o is used.

Rate-Axial

See "Axial Rate".

Rate-Radial

See "Radial Rate".

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Rate-Torsional

See "Torsional Rate".

Spring Rate

RIVERHAWK applies this term exclusively to express "TorsionalRate". Technically, however, since other rates are also through thesprings, they could be considered as Spring Rate", but it is not done.
See "Torsional Rate".

T LoadA load directed to the pivot such that the highest flexure stress istension.

Thrust Load

See "Axial Load".

Torsional Rate

The amount of torque necessary to rotate the pivot per unit of rotating
motion. This is generally in terms of pounds-inches per radian, butpound-inches per degree are also common usage. Designation is"K".

V LoadA radial load directed such that it bisects the crossed flexures and isperpendicular to the travel slots.

Page 6

H ys te re s is C u rv e - T yp e 4 0 0 S ta n d a rd P iv o t

1 0 -0 0
9 -0 0

7 -0 0
6 -0 0A v e ra g e
M a x im u m

5 -0 0
4 -0 0
3 -0 0
2 -0 0
1 -0 0

7-20

7-0

6-40

6-20

6-0

5-40

5-20

5-0

4-40

4-20

4-0

3-40

3-20

3-0

2-40

2-20

2-0

1-40

1-20

1-0

0-40

0-20

00-0

Hysteresis (min.-sec)

8 -0 0D e fle c tio n (d e g .-m in .)Page 7

0-0

15-0

14-40

14-20

14-0

13-40

13-20

13-0

12-40

12-20

12-0

11-40

11-20

11-0

10-40

10-20

10-0

9-40

9-20

9-0

8-40

8-20

8-0

7-40

7-20

7-0

6-40

6-20

6-0

5-40

5-20

5-0

4-40

4-20

4-0

3-40

3-20

3-0

2-40

2-20

2-0

1-40

1-20

1-0

0-40

0-20

Hysteresis (min.-sec.)

Hysteresis Curve - Type 600 Standard Pivot

19-00

18-00

17-00

16-00

15-00

14-00

13-00

12-00

11-00

10-009-00

Average
Maximum

8-00

7-00

6-00

5-00

4-00

3-00

2-00

1-00

0-

Deflection (deg.-min.)Page 8

H ysteresis C urve - T ype 800 Standard Pivot
38-00
36-00
34-00
32-00
30-00

Hysteresis (min.-sec.)

28-00
26-00
24-00
22-00
Average
Maximum

20-00
18-00
16-00
14-00
12-00
10-00
8-00
6-00
4-00
2-00
00

246

8

10

12

14

16

18

20

22

24

26

2830

Deflection (deg.)

Page 9

CENTERSHIFT vs. ANGULAR DEFLECTION
AT NO LOAD CONDITIONS
To determine centershift at any particular degree, multiply the diameter of the pivot by therespective factor shown below. For example, to determine the centershift of PN 5020-800(0.6250 inch diameter) at 4 degrees, multiply 0.6250 x 0.001 = 0.000625 inch.
Angle (Degrees)

Factor

10.00009

20.0003

30.0008

40.001050.001560.002070.004080.004590.0060

100.0071

110.0078

120.0085

130.0092

140.0100

150.0117160.0134170.0151

180.0168190.0185

200.0200

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Radial Load vs. Torsional Spring Rate
400300Percent of Spring Rate

2001000-100-200-30022. 52015105Vt (Applied Tension Load Lbs.)
x Constant

0510152025

Vc (Applied Compression Load Lbs.)
x Constant

Table of Constants**Pivot dia.

For Type 800*

For Type 600*

For Type 400*

0.1250

14.6

1.63

.204

0.1562

8.09

1.01

.126

0.1875

5.95

.743

.0895

0.2500

3.10

.387

.0485

0.3125

1.93

.241

.0309

0.3750

1.44

.173

.0217

0.5000

.784

.0980

.0123

0.6250

.450

.0576

.00720.07500

.326

.0404

.005050.8750

.247

.0298

.003721.0000

.180

.0228

.00286(inches)* This table applies only to standard pivots as defined herein.
** Diameter in inches.

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PIVOT STIFFNESS DATAWith reference to the flex pivot stiffness data provided in the “Dimensions andCharacteristics” table on page 2 of the Free Flex Pivot® catalog, it should be understoodthat this data is for reference only and RIVERHAWK does not guarantee that the productwill meet these values. The data was developed by empirical results (testing) obtained
via an assortment of pivot types and sizes over a period of time and represents theaverage values for the specific pivot groups tested. This testing was performed on thecantilever type pivot (5000 series) loaded at the midpoint of the unsupported half.
If cantilever pivots are used as a pair on a common axis and are interconnected with avery stiff piece of hardware, the radial stiffness value for each pivot can be assumed to be
1.25 times the value indicated in Table 1. This is a result of the moment (cantilever)bending being restrained, putting the pivot essentially in pure shear.
A double-ended (6000 series) pivot evenly loaded in the center of it’s length isapproximately 2.5 times the radial stiffness of an unsupported cantilever pivot, and thevalues in Table 1 can be increasing by a factor of 2.5.
The columns provided in Table 1 represent a specific load vector as related to the angularorientation of the load with respect to the pivot flexures as shown in Figure 1 and Figure
2. A simple way to remember the designations is that the subletter “c” means“compression” “t” means “tension”, and “a” means “axial”. “Compression” and “tension”
refer to compression or tension stresses in the pivot flexures resulting from the appliedload.
The “P” load is where the load is applied in line with the plane of a flexure. The “V” load iswhere the load vector is 45 degrees from the band between the flexures at the center of
one of the arc-shaped halves of the pivot. The “Pa” load is an axial load applied at thepivot centerline.
The data applies only to standard brazed construction pivots as listed in our catalog.
Special pivots must be considered independently.

Page 12TABLE 1
RADIAL AND AXIAL STIFFNESS DATABRAZED CANTILEVER PIVOTSCATALOG

RADIAL RATERADIAL RATERADIAL RATERADIAL RATEAXIAL RATENUMBER

Vc LOAD

Vt LOAD

Pc LOAD

Pt LOADPa LOAD(lb/in)(lb/in)(lb/in)(lb/in)(lb/in)5004-400
600
800

6,000
4,000
2,000

4,000
2,000
1,000

4,000
3,000
1,000

3,000
2,000
1,000

4,000
3,000
2,000

5005-400
600
800

8,000
6,000
3,000

6,000
4,000
2,000

7,000
4,000
2,000

5,500
3,000
2,000

8,000
5,000
3,000

5006-400
600
800

11,000
7,000
4,000

9,000
6,000
3,000

9,000
6,000
3,000

7,500
4,000
2,500

12,0008,000
4,000

5008-400600
800

16,00010,0005,000

14,0009,000
4,000

11,0006,000
4,000

20,00012,0007,000

5010-400
600
800

22,00013,0007,000

13,000
9,000
4,500
`
18,00012,0007,000

18,00012,0006,000

15,0009,000
5,000

26,00018,00010,0005012-400
600
800

27,00016,0009,500

22,00014,0008,000

23,00014,0007,000

19,00011,0006,000

34,00022,00012,0005016-400
600
800

38,00022,00012,00032,00020,00010,00032,00021,00010,00026,00016,0009,000

50,00032,00016,0005020-400
600
800

50,00029,00016,00040,00027,00013,00041,00026,00012,00035,000
20,00011,00064,00042,00022,0005024-400
600
800

61,00036,00020,00050,00033,00016,00051,00033,00015,00042,00025,00014,00079,00052,00026,0005032-400
600
800

83,00049,00027,00068,00045,00022,00070,00045,00021,00053,00034,00019,000110,000
71,00037,000

NOTE: 1. The stiffness data presented above applies only to cantilevered (5000 series) brazed
pivots loaded at the mid-point of the unsupported half at 0 degrees deflection.
2. For double-ended pivot (6000 series); multiply the Radial Stiffness values by 2.5 for thesame diameter and flexure class. There is no change in axial stiffness.
3. For a system of tandem-mounted cantilevered pivots (5000 series) connected very
stiffly, multiply the radial stiffness values by 1.25 for each pivot in the system.

Page 13

FIGURE 1
DOUBLE END SUPPORTED PIVOTSFIXED MOUNTPt

WHERE A Pt OR Vt CONDITION EXISTS A Pc OR Vc CONDITION MAY BE
OBTAINED BY ROTATING THE PIVOT 180 DEGREES OR CONVERSELY A Pt
OR Vt MAY BE OBTAINED FROM A Pc OR Vc LOADING BY ROTATING THE
PIVOT 180 DEGREES WITHIN FIXED MOUNT.

Page 14FIGURE 2CANTILEVER PIVOTSFIXED MOUNTPaLOADED MOUNTPc

FIXED MOUNTWHERE A Pt OR Vt CONDITION EXISTS A Pc OR Vc CONDITION MAYBE OBTAINED BY ROTATING THE PIVOT 180 DEGREES ORCONVERSELY A Pt OR Vt CONDITION MAY BE OBTAINED FROM A Pc
OR Vc BY ROTATING THE PIVOT 180 DEGREES IN THE FIXED MOUNT.

Page 15