Basic Equations for Parker Pneumatic Rotary Actuator
Mass Moments of Inertia Equations Table
Rectangular Prism Ix = 1/12m(b2 + c2) Iy = 1/12m(c2 + a2) Iz = 1/12m(a2 + b2 ) |
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Circular Cylinder Ix = 1/2ma2 Iy = Iz = 1/2m(3a2 + L2)
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Thin Rectangular Plate Ix = 1/12m(b2 + c2) Iy = 1/12mc2 Iz = 1/12mb2 |
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Circular Cone Ix = 3/10ma2 Iy = Iz = 3/5m(1/4a2 + h2)
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Sphere Ix = Iy = Iz = 2/5ma2 |
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Thin Disk Ix = 1/2mr2 Iy = Iz = 1/4mr2 |
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Parallel Axis Theorem Ip = ⌈ + md2
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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 |
Where:
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.)
Where:
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
Equations:
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
Available Pneumatic Cylinder Styles
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Tie Rod Cylinders | ![]() |
Guided Cylinders |
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Round Body Cylinders | ![]() |
Rodless Cylinders |
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Compact Cylinders |
Engineering & Product Selection Information
Pneumatic Product Selection
- Pneumatic Actuators & Air Cylinders
- Pneumatic Cylinders
- Automation Products: rotary actuators, grippers, slide tables, rotary tables, escapement
- Actuator Accessories: Linear alignment couplers, flow controls, air oil tanks, rodlocks, electronic sensors, shock absorbers
Application Engineering Data
- Operating Principles and Construction
- Fluids and Temperature
- Push and Pull Forces
- Mounting Information
- Ports
- Tie Rod Supports, Stroke Data & Stroke Adjusters
- Mounting Classes
- Stop Tubing
- Stroke Selection Chart
- Deceleration Force and Air Requirements
- Cushion Ratings and Air Requirements
- NFPA Rod End Data and Piston Rods
- Modifications, Special Assemblies, Tandem Cylinders, Duplex Cylinders
- Rotary Actuator Torque Requirements
- Rotary Actuator Basic Equations
- Conversion Factors
