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Sizing a Positioner: Payload, CG Offset, Overturning Moment, and Torque

A positioner is sized by where the load's center of gravity sits, not by its weight alone, and this article works one tilt-and-rotate positioner through from inputs to drive power. UTEC Industrial designs, engineers, machines, fabricates, and installs custom material handling systems for aerospace and heavy industry from its Spokane Valley, WA facility, integrating Allen-Bradley PLC and motion control with in-house CNC machining, heat treating, and stress relief. The example computes the combined center of gravity of a part and fixture, the gravity and inertia torque on the rotation and tilt axes, the overturning moment on the rotation bearing, the static stability of the base, and the drive power, then shows how the same numbers set the positioner's derating and its in-service monitoring. Every input is an illustrative assumption stated in the text, not a rating of any commercial positioner, and the method follows the chain design → engineering → parts machining → fabrication → assembly → weld fatigue → stress relief → drives → controls → tuning → monitoring from the first statics check to the drive data that confirms it.

What inputs are needed to size a positioner?​

A positioner cannot be sized from a single capacity figure. The loads on its drives and bearings depend on how far the payload's center of gravity (CG) sits from each axis, so the inputs are geometry as much as weight. The example below uses a two-axis tilt-and-rotate positioner carrying a machined aerospace housing in a welding and inspection fixture. All values are assumptions chosen to illustrate the method:

InputSymbolValue
Part weightW_p6,000 lb
Part CG height above table faceh_p24 in
Part CG offset from rotation axise_p7 in
Fixture weightW_f2,000 lb
Fixture CG height above table faceh_f8 in
Fixture CG offset from rotation axise_f3 in, same direction as the part
Tilt axis to table face distanceg8 in
Rotation bearing plane below table faces6 in
Rotating table weight, CG 4 in from tilt axisW_t2,500 lb
Payload radius of gyration about its own CGk24 in
Maximum rotation speed, reached inn_r, t_r1 rpm, 1 s
Maximum tilt speed, reached inn_t, t_t0.5 rpm, 1 s
Tilt rangeθ0° (table flat) to 135°
Positioner body weight, CG on tilt-axis verticalW_b6,000 lb
Tilt axis to base tipping edgeb30 in

Weights are in pounds-force, lengths in inches, and mass is found as m = W ÷ g_c with g_c = 386.1 in/s². The governing relations are the moment of a force about an axis, the location of a composite center of gravity, and the conditions of rigid-body equilibrium (Hibbeler 2021, Ch. 4, Ch. 5, and Ch. 9).

How is the combined center of gravity of part and fixture found?​

The part and fixture rotate together, so the drive sees their combined CG. A composite CG is the weight-weighted average of the individual CG locations, x̄ = Σ(W_i × x_i) ÷ ΣW_i, applied separately in each direction.

  • Combined payload weight: W = 6,000 + 2,000 = 8,000 lb
  • Combined CG height: h = (6,000 × 24 + 2,000 × 8) ÷ 8,000 = (144,000 + 16,000) ÷ 8,000 = 20 in above the table face
  • Combined CG offset: e = (6,000 × 7 + 2,000 × 3) ÷ 8,000 = (42,000 + 6,000) ÷ 8,000 = 6 in from the rotation axis

Two practical points follow. First, the fixture is part of the payload; ignoring a 2,000 lb fixture here would understate the payload by 25 percent and misplace the CG by 4 in in height. Second, the part's CG is rarely known exactly. For a weldment it comes from the CAD model, and for a casting or a part with internal cavities the model may be off. A sound specification gives the CG as a range, and the calculation is run at the worst corner of that range. A common failure mode is a positioner sized for the nominal CG and then loaded with a part whose real CG sits farther out (Hibbeler 2021, Ch. 9).

What rotation torque does the CG offset create?​

When the table is tilted, the rotation axis is no longer vertical, and gravity acting at the offset CG produces a torque about that axis. The peak gravity torque over one revolution, reached when the rotation angle puts the offset horizontal, is T_g = W × e × sin θ, where θ is the tilt of the table from horizontal. It is zero with the table flat and largest when the table is tilted to 90°:

  • θ = 0°: T_g = 0
  • θ = 45°: T_g = 8,000 × 6 × 0.7071 = 33,941 lb·in
  • θ = 90°: T_g = 8,000 × 6 × 1.0 = 48,000 lb·in (4,000 lb·ft)
  • θ = 135°: T_g = 8,000 × 6 × 0.7071 = 33,941 lb·in

The design value is the 90° figure, 48,000 lb·in, because the tilt range passes through 90°. That torque must be supplied by the drive to lift the CG, and resisted by the drive and brake when lowering it, at the worst rotation angle of every revolution. The torque is also proportional to e: doubling the CG offset to 12 in doubles the torque to 96,000 lb·in with no change in weight, which is why CG offset is a first-class input rather than a detail (Hibbeler 2021, Ch. 4).

How much torque does acceleration add to the rotation axis?​

Starting and stopping the rotation takes torque in addition to gravity torque, T_i = I × α, where I is the mass moment of inertia about the rotation axis and α is the angular acceleration.

  • Payload mass: m = 8,000 ÷ 386.1 = 20.72 lb·s²/in
  • Inertia about the payload's own CG: I_cg = m × k² = 20.72 × 24² = 11,935 lb·in·s²
  • Parallel-axis transfer to the rotation axis: I = I_cg + m × e² = 11,935 + 20.72 × 6² = 12,681 lb·in·s²
  • Top speed: ω = 1 rpm × 2π ÷ 60 = 0.1047 rad/s, reached in 1 s, so α = 0.1047 rad/s²
  • Inertia torque: T_i = 12,681 × 0.1047 = 1,328 lb·in

The total rotation torque at the worst tilt is 48,000 + 1,328 = 49,328 lb·in (4,111 lb·ft), before friction, gear efficiency, and service factor. At this low speed, inertia adds only about 2.8 percent, and gravity torque dominates.

That changes at an emergency stop. If the same axis is brought from 1 rpm to rest in 0.1 s, α rises tenfold to 1.047 rad/s² and T_i becomes 13,279 lb·in, about 28 percent of the gravity torque, applied suddenly through the gear train. A gear train sized for normal ramps alone can be overloaded by repeated hard stops, so the stopping case belongs in the sizing, and a controlled stop that ramps the axis down before removing torque is gentler on the gearing than an uncontrolled one (Hibbeler 2021, Ch. 10; Budynas and Nisbett 2019, Ch. 16).

What torque does the tilt axis need?​

The tilt axis carries the whole payload at a much longer arm than the rotation axis, because the arm includes the CG height above the table and the distance from the tilt axis to the table face. With the table flat, the payload CG sits g + h = 8 + 20 = 28 in above the tilt axis and e = 6 in to one side (worst case: the offset lies in the tilt plane).

  • Payload arm from tilt axis: r = √(28² + 6²) = √820 = 28.64 in
  • Maximum payload gravity torque, when that arm is horizontal: 8,000 × 28.64 = 229,085 lb·in
  • Table gravity torque, added conservatively as if aligned: 2,500 × 4 = 10,000 lb·in
  • Tilt gravity torque: T_tilt,g = 239,085 lb·in (19,924 lb·ft)

The arm is 12.1° from the table normal (tan⁻¹ of 6 ÷ 28), so it becomes horizontal at a tilt of about 77.9° or 102.1°, depending on which side the offset lies; both are inside the 0° to 135° range, so the maximum is reachable.

The inertia term is small again. The payload's inertia about the tilt axis is m × (k² + r²) = 20.72 × (576 + 820) = 28,925 lb·in·s², plus about 104 lb·in·s² for the table treated as a point mass, for 29,029 lb·in·s². At 0.5 rpm reached in 1 s, α = 0.0524 rad/s² and T_i = 1,520 lb·in. The total tilt torque is about 240,605 lb·in (20,050 lb·ft), roughly 4.9 times the rotation torque. The CG height, not the CG offset, sizes the tilt drive; each additional inch of CG height adds about 7,800 lb·in of tilt torque on this payload (Hibbeler 2021, Ch. 4 and Ch. 10).

What overturning moment does the rotation bearing see?​

The slewing bearing under the table carries axial load, radial load, and an overturning (tilting) moment, and all three change with tilt angle. The moment arm for the axial component is the in-plane offset e; the arm for the radial component is the CG height above the bearing plane, h + s = 20 + 6 = 26 in.

  • Table flat, θ = 0°: axial load 8,000 lb, radial load 0, overturning moment M = 8,000 × 6 = 48,000 lb·in
  • Table at 90°: axial load 0, radial load 8,000 lb, overturning moment M = 8,000 × 26 = 208,000 lb·in (17,333 lb·ft)
  • Worst intermediate angle: with the offset aligned in the tilt plane, M(θ) = W × (e × cos θ + 26 × sin θ), which peaks where tan θ = 26 ÷ 6, at θ ≈ 77°, giving M = 8,000 × √(6² + 26²) = 213,467 lb·in (17,789 lb·ft)

The governing bearing moment is about 4.4 times the table-flat value. A bearing selected from the flat condition alone, which is a common sizing error on tilt-and-rotate machines, would be loaded beyond its selection case as soon as the table began to tilt, and to about 4.4 times that case near 77°. Rolling-bearing selection checks the combined radial and thrust loads against the manufacturer's catalog ratings; for a slewing bearing, the manufacturer's load chart is checked with the combined axial load, radial load, and overturning moment at each tilt angle, and the bearing's mounting bolts and the table and housing structure are designed for the same combination (Hibbeler 2021, Ch. 4; Budynas and Nisbett 2019, Ch. 11).

Will the positioner base tip over?​

The whole positioner must stay upright when the payload is tilted out over its base. The static test is whether the combined CG of payload, table, and body stays inside the tipping edge of the footprint.

At the worst tilt, the payload CG is 28.64 in horizontally from the tilt axis, and the table CG is conservatively taken as 4 in out in the same direction. The body's CG is on the tilt-axis vertical line. The combined horizontal CG position is:

x̄ = (8,000 × 28.64 + 2,500 × 4 + 6,000 × 0) ÷ (8,000 + 2,500 + 6,000) = 239,085 ÷ 16,500 = 14.49 in

That is well inside the 30 in tipping edge, so the base is statically stable in this configuration. Solving the same equation for the payload arm that would put x̄ exactly at the edge gives (30 × 16,500 − 10,000) ÷ 8,000 = 60.6 in, so this payload would have to sit more than twice as far out before the unanchored base tipped under static load.

A static margin is not the whole answer. Emergency stops, a part striking the fixture while being landed by crane, and an operator fouling a moving table all add loads that a static check does not include. The risk assessment identifies those cases, and the anchorage is designed for them (Hibbeler 2021, Ch. 5; ISO 12100:2010).

How are drive power, gearing, and brakes selected from these torques?​

Power at the output of each axis is torque times angular velocity, P = T × ω:

  • Rotation: 49,328 lb·in × 0.1047 rad/s = 5,166 lb·in/s = 430 ft·lb/s, or 430 ÷ 550 = 0.78 hp at the output
  • Tilt: 240,605 lb·in × 0.0524 rad/s = 12,598 lb·in/s = 1,050 ft·lb/s, or 1.91 hp at the output

These are outputs before gear efficiency, friction, and service factor, so the installed motors are larger. The very low output speeds call for high reduction. Assuming a motor base speed of 1,750 rpm, the rotation axis needs a total ratio of 1,750 ÷ 1 = 1,750:1 and the tilt axis 1,750 ÷ 0.5 = 3,500:1, usually split between an enclosed reducer and an open pinion on the slewing-ring gear. The ideal motor torque, before dividing by the train efficiency from the reducer manufacturer's data, is 49,328 ÷ 1,750 = 28.2 lb·in for rotation and 240,605 ÷ 3,500 = 68.7 lb·in for tilt.

  • Gearing. The enclosed reducer is rated as an industrial enclosed gear drive under ANSI/AGMA 6013-B16, and open spur or helical gearing on the slewing ring is rated for pitting and bending under ANSI/AGMA 2001-D04. The service factor for the application comes from the reducer manufacturer's selection data, and no value is assumed here.
  • Brakes. A horizontal-axis load with CG offset back-drives the gear train when torque is removed. The tilt brake must hold at least the 239,085 lb·in static gravity torque at the output, or about 68.3 lb·in reflected to a motor-mounted brake through the 3,500:1 train before efficiency, plus the design margin the designer selects. Back-driving efficiency differs from forward efficiency, so the brake is checked through the train in the back-driving direction.

UTEC Industrial builds positioner drive packages with VFD or servo drives, Allen-Bradley ControlLogix or CompactLogix control, and UL 508A panels (ANSI/AGMA 6013-B16; ANSI/AGMA 2001-D04; Budynas and Nisbett 2019, Ch. 3 and Ch. 13).

Why is a positioner's rated capacity not its usable capacity at every CG?​

A positioner capacity quoted as a single weight carries hidden assumptions about CG offset and CG height. The worked numbers show why. The rotation drive in this example was sized for 48,000 lb·in of gravity torque, so its allowable payload is W_allow = 48,000 ÷ e:

CG offset eAllowable payload on rotation torque
3 in16,000 lb, then likely limited by bearing or tilt capacity
6 in8,000 lb, the design case
9 in5,333 lb
12 in4,000 lb

The tilt axis derates with CG height. Holding the table's 10,000 lb·in share constant, the tilt drive has 229,085 lb·in available for payload. If the part's CG rises from 20 in to 30 in above the table, the arm becomes √(38² + 6²) = 38.47 in and the allowable payload falls to 229,085 ÷ 38.47 = 5,955 lb, a 26 percent reduction for a 10 in change in CG height.

A common failure mode is a buyer reading the headline weight and mounting a tall or off-center part within that weight but outside the CG envelope. The result can be a stalled drive, an overheated motor, or a table that creeps under its brake. A usable capacity statement is therefore a curve or table of payload against CG offset and CG height, one per axis, with the bearing's combined-load limit shown alongside (Hibbeler 2021, Ch. 4).

How are the shafts, welds, and frame checked against these loads?​

The torques and moments above become stresses in the shafts, welds, and frame. For a solid circular shaft in torsion, shear stress is τ = 16T ÷ (πd³). Assuming a 5 in diameter tilt shaft carrying the full 240,605 lb·in:

τ = 16 × 240,605 ÷ (π × 5³) = 3,849,680 ÷ 392.7 = 9,803 psi

That value is combined with the bending stress from the shaft's bearing reactions using the distortion-energy (von Mises) equivalent stress, σ' = √(σ² + 3τ²), and compared with the chosen material's strength with an appropriate design factor. The allowable stress depends on material and heat treatment, so no allowable is assumed here.

Fatigue governs parts whose stress reverses. When the table is tilted and rotating, the offset load sweeps around the slewing-bearing mounting, the table spindle, and the welds that attach the housing to the tilt cradle, reversing once per revolution. AWS D14.4/D14.4M:2019 is the specification for welded joints in machinery and equipment and is the natural basis for these weld details. Bearing mounting faces and bores must also stay flat and true, so heavy positioner frames are commonly stress-relieved before final machining to keep residual welding stress from distorting them (Budynas and Nisbett 2019, Ch. 3, Ch. 5, and Ch. 6; AWS D14.4/D14.4M:2019).

How do sensing and controls confirm the sizing assumptions in service?​

The sizing rests on an assumed weight and CG. The drive and sensors can check those assumptions every time a part is loaded, which closes the loop between the calculation and the machine on the floor:

  • Torque-based CG check. Servo drives such as the Allen-Bradley Kinetix 5700 close a current loop on the motor, and motor current relates to motor torque, so the drive reports holding torque. With the table tilted to 90°, the measured gravity torque on the rotation axis divided by the payload weight gives the actual offset. If the drive reports 60,000 lb·in (referred to the output) on an 8,000 lb payload, e = 60,000 ÷ 8,000 = 7.5 in, 25 percent beyond the 6 in design case, and the PLC can block further tilting until the part is re-fixtured.
  • Weight check. Load cells in the table supports or fixture measure payload weight directly, so both terms of W × e are measured rather than assumed.
  • Position and limits. Absolute encoders on both axes let the PLC enforce a CG-dependent tilt limit, stopping a tall payload short of the angle where its torque would exceed the drive rating.
  • Safety functions. Kinetix 5700 drives include safe torque-off. Safety logic runs in the safety task of a GuardLogix controller; Rockwell Automation rates a GuardLogix 5580 primary controller with a safety partner for applications up to SIL 3 and PL e (Cat. 4), and up to SIL 2 and PL d (Cat. 3) without one. Standard logic runs in Logix 5000 continuous, periodic, and event tasks. ISO 13849-1:2023 is the standard for the design of safety-related parts of control systems, and IEC 60204-1:2016 covers the machine's electrical equipment from the supply connection onward.
  • Tuning at load. The Kinetix 5700 commissioning procedure includes a tuning step for each axis, and autotuned bandwidths can require adjustment once motor and load are connected, so the axes are tuned with a representative loaded payload.

UTEC Industrial, a Rockwell Automation Recognized System Integrator, commissions and tunes these axes with the loaded part during factory acceptance testing and on-site commissioning (Rockwell Automation 2198-UM002E-EN-P, Kinetix 5700; Rockwell Automation 1756-RM012J-EN-P-2025; Rockwell Automation 1756-RM094N-EN-P-2025; ISO 13849-1:2023; IEC 60204-1:2016).

What assumptions does this worked example make, and where do they break?​

Every number above follows from the stated inputs. The assumptions, and what happens when each fails, are:

  • Rigid payload and fixture. A flexible part deflects, which moves its CG outward and adds to e; long, slender parts may need a headstock-tailstock layout instead.
  • Worst-case alignment. The part and fixture offsets are taken in the same direction, and the table CG is added to the tilt torque as if aligned; this is conservative.
  • Radius of gyration of 24 in. The inertia terms scale with k², so a part spread farther from its CG raises the acceleration and stopping torques; here they stayed small only because speeds are low.
  • Ramp times of 1 s, and 0.1 s for the emergency-stop case. Shorter ramps raise inertia torque in direct proportion.
  • Ideal gearing. Motor torques are shown before efficiency; real trains need more motor torque, and back-driving efficiency governs the brake check.
  • No friction, seal drag, cable-carrier drag, or welding-lead drag. These are added from component data.
  • Static base check. Dynamic, impact, and seismic loads are assessed separately in the risk assessment.
  • Shaft stress without allowable. The 9,803 psi torsional stress is compared with a material allowable and a fatigue check chosen for the actual shaft.

A positioner specified with a CG range rather than a point, and checked at each corner of that range on every axis, avoids most of the failures these assumptions hide (Hibbeler 2021, Ch. 5 and Ch. 9; Budynas and Nisbett 2019, Ch. 1).

Related Articles

References​

  • Hibbeler, R.C. Engineering Mechanics: Statics, 15th ed. Pearson, 2021. ISBN 9780137514663.
  • Budynas, R.G. and Nisbett, J.K. Shigley's Mechanical Engineering Design, 11th ed. McGraw-Hill, 2019. ISBN 9780073398211.
  • ANSI/AGMA 6013-B16 (R2021): Standard for Industrial Enclosed Gear Drives. AGMA, 2016.
  • ANSI/AGMA 2001-D04 (R2016): Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth. AGMA, 2004.
  • AWS D14.4/D14.4M:2019: Specification for the Design of Welded Joints in Machinery and Equipment. AWS, 2019.
  • ISO 12100:2010: Safety of machinery — General principles for design — Risk assessment and risk reduction. ISO, 2010.
  • ISO 13849-1:2023: Safety of machinery — Safety-related parts of control systems — Part 1: General principles for design. International Organization for Standardization, 2023.
  • IEC 60204-1:2016 (Ed. 6.0): Safety of Machinery -- Electrical Equipment of Machines -- Part 1: General Requirements. International Electrotechnical Commission, 2016.
  • Rockwell Automation 2198-UM002E-EN-P (2018): Kinetix 5700 Servo Drives User Manual. Rockwell Automation, 2018.
  • Rockwell Automation 1756-RM012J-EN-P-2025: GuardLogix 5580 and Compact GuardLogix 5380 Controllers Safety Reference Manual. Rockwell Automation, 2025.
  • Rockwell Automation 1756-RM094N-EN-P-2025: Logix 5000 Controllers Design Considerations. Rockwell Automation, 2025.

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