Pneumatic Rotary Actuator Sizing-Selecting Tools

Parker Pneumatic Rotary Actuators



Single or double vane rotary actuator

PRN_rotary_actuator_zm 250x250


Single or double vane rotary actuator



Rack and pinion rotary actuator



Rack and pinion rotary actuator with optional feed control

HP Good


Rack and pinion rotary actuator

Types of Rotary Actuators

Pneumatic Vane  
  • Good mechanical efficiency
  • Little, if any, backlash
  • Highest torque to weight ratio
  • Internal cross vane leakage(bypass)
  • Small rotary group mass moment of inertia.
  • Good for high speed applications
  • Economical
  • Compact
Rack and Pinion
  • Compact conversion of linear to rotary motion
  • Female bore or male shafts
  • Backlash (Anti-backlash option on PTR)
  • Long seal life
  • Large pinion bearings
  • Can be used as pillow block
  • High cycle life


Shaft Loads

Design Torque

Design torque represents the maximum torque than an actuator must supply in an application. This maximum is the greater of the Demand Torque or the Cushion Torque. If the demand torque exceeds what the actuator can supply, the actuator will either move too slowly or stall. If the cushion torque is too high, the actuator may be damaged by excessive pressure. Demand torque and cushion torque are defined below in terms of load, friction and acceleration torque, along with equations for calculating demand torque and cushion torque for some general applications.

T - Torque
The amount of turning effort exerted by a rotary actuator.

TD - Demand Torque
The torque required from the actuator to do the job - the sum of the load torque, friction torque and acceleration torque, multiplied by an appropriate design factor. Design factors vary with the applications and the designers' knowledge.

TD = Tα  + Tf + TL

TL - Load Torque
The torque required to equal the weight or force of the load. The load torque term is intended to encompass all torque components that aren't included in the friction or acceleration terms.

Tf - Friction Torque
The torque required to overcome friction between any moving parts, especially bearing surfaces.

Tf = μWr

Tα - Acceleration Torque
The torque required to overcome the inertia of the load in order to provide a required acceleration or deceleration. See the Rotary Actuators Basic Equations page for more information regarding mass moments of inertia and equations for determining acceleration (α).

Tα = Iα

TC - Cushion Torque
The torque that the actuator must apply to provide a required deceleration. This torque is generated by restricting the flow out of the actuator (meter-out) to create a back pressure which decelerates the load. This back pressure/deceleration often must overcome both the inertia of the load and the driving pressure (system pressure) from the pump.

TC = Tα + PrV/θ - Tf ± TL

The friction torque Tf reduces the torque the actuator must apply to stop the load. The load torque TL may add to, or subtract from the torque required from the actuator, depending upon the orientation of the load torque. For example, a weight being swung upward would result in a load torque that is subtracted.

WARNING: Rapid deceleration can cause high pressure intensification at the outlet of the actuator. Always insure that cushion pressure does not exceed the manufacturer's pressure rating for the actuator.

KE - Kinetic Energy (1/2 Jmω2)
The amount of energy that a rotating load has. The rotator must be able to stop the load. All products have kinetic energy rating tables. Choose the appropriate deceleration option (i.e., bumper, cushions, shock absorbers, etc.) that meets or exceeds the kinetic energy of the load.

Example 1:

TD = Tα  + Tf + TL

Tα = 0

Tf = 0

TL = (500 lb)(10 in) = 5,000 lb-in

TD = 5,000 lb-in

 Demand Torque Example 1

Example 2:

(The 500 lb rotating index table is supported by bearings with a coefficient of friction of 0.25. The table's acceleration is at 2 rad/sec2. The table's mass moment of inertia is 2,330 lb-in-sec2.)

TD = Tα  + Tf + TL

Tα = Iα = (2,330 lbs-in-sec2)(2/sec2) = 4,660 lb-in

Tf = μWrb = 0.25 (500 lb)(55 in) = 6,880 lb-in

TL = 0

TD = 4,660 lb-in + 6,880 lb-in = 11,540 lb-in


Example 3:

TD = Tα  + Tf + TL

Tα = 0

Tf = 0

TL = (500 lb)(10 in) = 5,000 lb-in

TD = 5,000 lb-in



Mass Moments of Inertia Equations Table

Rectangular Prism

Ix = 1/12m(b2 + c2)

Iy = 1/12m(c2 + a2)

Iz = 1/12m(a2 + b2 )

 Rectangular Prism

Circular Cylinder

Ix = 1/2ma2

Iy = Iz = 1/2m(3a2 + L2)



Thin Rectangular Plate

Ix = 1/12m(b2 + c2)

Iy = 1/12mc2

Iz = 1/12mb2

 Thin Rectangular Plate

Circular Cone

Ix = 3/10ma2

Iy = Iz = 3/5m(1/4a2 + h2)




Ix = Iy = Iz = 2/5ma2


Thin Disk

Ix = 1/2mr2

Iy = Iz = 1/4mr2

Thin Circular Disk 

Parallel Axis Theorem

Ip = ⌈ + md2


Parallel Axis Theorem 

Ip = Mass moment of inertia about an axis parallel to a centroidal axis

⌈ = Mass moment of inertia about a centroidal axis

m = Mass

d = Distance between axes


t = time

θ = angular position

ωt = angular velocity at time = t

ω0 = angular velocity at time = 0

α = angular acceleration

When Acceleration Is Constant:

θ = ω0t + 1/2αt2 ;   α = 2θ/t2

θ = ω0t + 1/2ωtt ;  α = (ωt - ω0)2/2θ

ω = (ω02 + 2αθ)1/2 ; α = (ωt - ω0)/t

When Velocity Is Constant:

 θ = ωt

Basic Velocity, Acceleration, Kinetic Energy and Torque Equations

(The equations below are based on triangular velocity profile.)


Θ = Angle of rotation (degrees)

t = Time to rotate through Θ (sec)

ω = Angular velocity, radians/sec

α = Angular accelerations (radians/sec2)

WL = Weight of load (lbf)

Ta = Torque to accelerate load (lb-in)

Us = Coefficient of static friction

Jm* = Rotational mass moment of inertia (lb-in-sec2)

Tf = Torque to overcome friction (lb-in)

TL = Torque to overcome effects of gravity

* Use "I" values from the Mass Moments of Inertia table


ωmax = 0.35 x Θ/t

α = ωmax2/ (Θ/57.3)

α = ωmax/(t/2)

K.E. = 1/2 Jmω2

Ta = α x Jm

Tf = W x Us x (Distance from pivot point to center of external bearings)

TL = (Torque arm length to C.G. of load) x WL x cos (Φ)

(Where Φ = Angle between torque arm and horizontal plane)

Coefficients of Friction

Material* μs μk
Steel on steel 0.80 0.40
Steel on steel (lubricated) 0.16 0.03
Aluminum on steel 0.45 0.30
Copper on steel 0.22 0.22
Brass on steel 0.35 0.19
PTFE on steel 0.04 0.04

*Dry contact unless noted

Parker rotary actuators provide output torque up to 10,000 lb-in. The chart below shows the nominal torque output range of various actuator models at 100 psi.

Caution: This chart is intended as a guide only. Refer to actual product data pages before specifying an actuator. Factors such as pressure rating, rotation and actual torque output may be affected by specific product details and options.

Nominal Torque at 100 PSI

Output Torque (lb-in) Rotation < 95° Rotation > 100°
Vane Models Rack & Pinion Models Vane Models Rack & Pinion Models
10000   HP10   HP10
5000   HP4.5   HP4.5
3000 PRN800D B6714   B6714
2500   PTR322   PTR322
2000 PV46D      
1500 PRN800S   PRN800S  
1250 PV44D PTR321, B6713   PTR321, B6713
900 PRN300D PTR252 PV46 PTR252
700 PV36D, PV42D      
600   PTR202, B6712 PV44 PTR202, B6712
500 PV42D, PRN150D PTR251   PTR251
400 PV33D, PRN300S   PV36, PRN300S  
300   PTR201 PV42 PTR201
250   PTR152   PTR152
200 PRN150S   PV33, PRN150S  
150 PV22D, PRN50D PTR151, B6711   PTR151, B6711
100 PRN30D      
80   PTR102 PV22 PTR102
60 PRN50S   PRN50S  
40 PRN30S PTR101 PRN30S PTR101
35 PV11D      
25 PRNA20S   PRNA20S  
20 PV10D      
15 PRNA10S   PV11, PRNA10S  
10     PV10  



Force Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

oz 1 0.0625 0.2780 0.0284
lbf 16 1 4.4482 0.4536
N 3.5970 0.2248 1 0.1020
kg(f) 35.2740 2.2050 9.8068 1

Torque Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

1 0.0625 52083E-03 7.0616E-03
16 1 0.0833 0.1130
lb-ft 192 12 1 1.356
Nm 141.61 8.8507 0.7376 1

Rotational Inertia Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

oz-in2 oz-in-sec2 lb-in2 lb-in-sec2 lb-ft2 lb-ft-sec2 kg-m2 kg-m-sec2 kg-cm2 kg-cm-sec2
1 2.5900E-03 6.2500E-02 1.6190E-04 4.3403E-04 1.3490E-05 1.8290E-05 1.8650E-06 1.8290E-01 1.8650E-04
3.8610E+02 1 2.4130E+01 6.2500E-02 1.6760E-01 5.2080E-03 7.0620E-03 7.2010E-04 7.0620E+01 7.2010E-02
lb-in2 1.6000E+01 4.1442E-02 1 2.5900E-03 6.9444E-03 2.1583E-04 2.9260E-04 2.9840E-05 2.9260E+00 2.9840E-03
lb-in-sec2 6.1767E+03 1.6000E+01 3.8610E+02 1 2.6810E+00 8.3333E-02 1.1300E-01 1.1520E-02 1.1300E+03 1.1520E+00
lb-ft2 2.3040E+03 5.9666E+00 1.4400E+02 3.7300E-01 1 3.1080E-02 4.2140E-02 4.2970E-03 4.2140E+02 4.2970E-01
lb-ft-sec2 7.4129E+04 1.9201E+02 4.6333E+03 1.2000E+01 3.2175E+01 1 1.3560E+00 1.3824E-01 1.3560E+04 1.3824E+01
kg-m2 5.4675E+04 1.4160E+02 3.4176E+03 8.8496E+00 2.3730E+01 7.3746E-01 1 1.0190E-01 1.0000E+04 1.0190E+01
kg-m-sec2 5.3619E+05 1.3887E+03 3.3512E+04 8.6806E+01 2.3272E+02 7.2338E+00 9.8135E+00 1 9.8130E+04 1.0000E+02
kg-cm2 5.4675E+00 1.4160E-02 3.4176E-01 8.8496E-04 3.3730E+03 7.3746E-05 1.000E-04 1.0191E-05 1 1.0190E-03
kg-cm-sec2 5.3619E+03 1.3887E+01 3.3512E+02 8.6806E-01 2.3272E+00 7.2338E-02 9.8135E-02 1.0000E-02 9.8135E+02 1

Length/Distance Conversion Factors

Multiply value A by conversion factor in table to calculate value B.

cm m
in 1 0.0833 25.4 2.54 0.0254
ft 12 1 304.8 30.48 0.3048
mm 0.03937 0.00328 1 0.1 0.001
cm 0.3937 0.03281 10 1 0.01
m 39.37 3.281 1000 100 1



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