Machine Design #25: Locating in Machine Design — From the 3-2-1 Principle to Dowel Pins and Zero-Point Systems

A part machined to the correct dimensions but placed in the wrong position is still a defective part. A mechanism with precise linear guides, a good servo and a high-resolution encoder can still repeat poorly, resist assembly and need constant on-site adjustment if the locating datum was chosen badly.

In machine design, "locating" is not just picking a pin to drop into a hole. It is the process of deciding:

Where the part must sit relative to the machine coordinate system.
Which motions must be locked and which must be allowed to remain.
Which datum directly determines the function of the product.
How machining error, assembly clearance, temperature, clamping force and wear enter the error chain.
Whether the mechanism still holds its position after thousands of load and unload cycles.

This article organizes the locating principles and methods commonly used in machine design, fixtures, moulds, automation stations and precision equipment. The focus is not on listing components, but on choosing the right principle for each set of working conditions.

1. Start from six degrees of freedom

A rigid body in space has six degrees of freedom, usually written 6-DoF:

Translation along X.
Translation along Y.
Translation along Z.
Rotation about X, or roll.
Rotation about Y, or pitch.
Rotation about Z, or yaw.

Locating is the deliberate constraint of these degrees of freedom. Fully fixing a part means locking all six. Conversely, a bearing must allow rotation about one axis while locking the rest; a linear guide must allow translation in one direction while restricting the other five.

So before choosing a pin, bushing, rest pad or clamping mechanism, the designer has to answer two questions:

Which degrees of freedom must be locked for the machine to perform its function?
Which degrees of freedom must be preserved to avoid jamming, absorb error or allow motion?

Many mechanisms that are hard to assemble are not suffering from tight tolerances. They are suffering from the same degree of freedom being locked more than once.

2. The 3-2-1 principle: the foundation of fixtures and assembly

The 3-2-1 principle is the most common way of locking all six degrees of freedom of a prismatic part with the minimum number of contact points.

2.1 Three points on the primary datum

Three rest points on the bottom face establish the primary datum. They constrain:

Translation perpendicular to the datum face.
The two rotations that tilt the part off the datum.

Three points always establish a plane. If four rigid points are used while neither the part face nor the fixture face is perfectly flat, one of the four may not make contact, or the part will be bent when clamped.

2.2 Two points on the secondary datum

Two rest points on a side face constrain:

One translation within the primary datum plane.
The one remaining rotation about the normal to the primary datum.

The greater the distance between the two points, the better the resistance to rotation and the lower the sensitivity to clearance. This is also why two locating pins should generally be placed as far apart as the structure allows.

2.3 One point on the tertiary datum

The last point stops the remaining translation. Once the 3-2-1 contacts are established, the part has a geometrically defined position.

Locating, however, is not the same as holding. The part can still leave its datum faces if external forces or vibration break the contact. Clamping force therefore has to be added in a direction that pushes the part back onto the chosen datums.

Practical rule: the locating elements determine the position; the clamping elements only maintain contact with the datums. Never use clamping force to "pull" a part into the desired position.

3. Choose the contact type from the surface condition

No single rest type suits every part. Hardness, flatness, roughness, coatings, burrs and cleanliness all determine whether to use point, line or area contact.

Surface condition	Suitable contact	Benefit	Risk to control
Ground surface, hardened steel, good flatness	Hard rest button, ball or local contact	Clear datum point, good repeatability, insensitive to a thin oil film	High contact stress; needs wear resistance and indentation checks
Normal milled surface	Small rest faces or separate rest pads	Stiff, good load capacity, easy to make	Dust, chips and warp prevent full seating
Cast, forged or scaled surfaces	Adjustable rest screws, serrated tips, hard contact points	Penetrates an uneven surface layer and creates a clear datum	Can mark the surface; the height of each point must be controlled
Aluminium, plastic, painted or soft-plated surfaces	Wide rest pads, softer intermediate material	Lower surface pressure, fewer indentation marks	Large areas trap dust; pad material can age
Thin parts	Rests distributed near the clamping and machining zones	Less deflection, less vibration	Too many rigid points easily cause over-constraint

3.1 "Point contact" does not mean a sharp tip in every case

In precision design, a rest point is usually a small contact zone with defined geometry and a material hard enough for the job. It does not mean always using a genuinely sharp needle. Too sharp a tip creates high contact stress and easily sinks into aluminium, plastic or an unhardened face.

For high loads, use a hardened rest button with a small spherical face or a flat face of limited diameter. The goal is to make the contact position unambiguous while keeping surface pressure within limits.

3.2 Large rest faces give high stiffness but demand cleanliness

Large rest faces suit high loads and resistance to deflection. The drawback is that a single small chip can lift the whole part. Where good repeatability is needed:

Break the rest face into pads of just sufficient area.
Add chip escape grooves and space for dust to collect.
Provide air blow or a cleaning procedure before loading.
Avoid using the entire base face as a datum unless it is genuinely necessary.

3.3 Locator material, heat treatment and surface finish

Locators, pins and rest buttons are small parts, but they usually take repeated contact loads. Untreated soft steel will quickly flatten, score or raise a burr, and the position will drift over time.

Practical selection generally follows these rules:

Use hardenable steel for pins and rest faces that are loaded and unloaded often.
Finish-grind after heat treatment on the surfaces that determine position.
In abrasive dust or sliding-load environments, consider a suitable wear-resistant coating.
In humid environments or with cutting fluid, prevent rust and never allow rust to form on the datum face itself.
Do not paint, heavily anodize or apply uncontrolled plating to a surface used as a precision datum. If surface treatment is unavoidable, the coating thickness has to be inside the tolerance chain.
Excessive roughness makes the position vary with the tool-mark direction; very low roughness on an insufficiently flat surface still fails to create a good datum. Roughness, flatness and machining method have to be controlled together.

For soft parts, deliberately make the locator the harder and replaceable element. Conversely, where the product surface must not be marked, use a sacrificial pad or an insert softer than the product and accept periodic pad replacement instead of damaging the product.

4. Exact constraint versus over-constraint

Two design mindsets are common: constraining exactly the right number of degrees of freedom, and deliberately using many contact points to increase stiffness.

4.1 Kinematic design: exactly and sufficiently constrained

Kinematic design, or exact-constraint design, uses precisely the number of contacts needed to lock six degrees of freedom without creating redundant constraint.

Classic configurations include:

One ball in a conical seat, one ball in a V-groove and one ball on a flat.
Three balls in three V-grooves arranged around a centre.
Variants using balls, cones, grooves and precisely machined datum faces.

Main advantages:

Very good positional repeatability.
Little assembly stress from dimensional error.
Less sensitivity to differing thermal expansion between parts.
Easy to identify the load path and the sources of error.

Disadvantages:

Small contact areas, so load capacity and stiffness are usually lower than a multi-contact mechanism.
Hertzian pressure at the contact zone can be high.
Requires hard materials, good surfaces and wear control.

Kinematic couplings are common in optical, metrology and semiconductor equipment — assemblies that must be removed and refitted yet return to position at the micrometre level or better.

4.2 Elastic averaging: many contacts to average out error

Elastic averaging uses more contacts than the minimum. Local error at each point is distributed and averaged out through very small elastic deformation of the material.

Hirth and Curvic couplings are typical examples. Two faces with many radial teeth engage simultaneously. Each tooth may carry a small error, but the full ring of teeth produces:

High torsional stiffness.
High load capacity.
Good angular repeatability.
Load distributed over many contact zones.

This works well when tooth geometry, concentricity, flatness and clamping force are well controlled. If errors are too large or the clamping force is uneven, the mechanism can lock in a distorted state, generate internal stress or contact on only a few teeth.

Criterion	Exact constraint	Elastic averaging
Number of contacts	Minimum to lock 6 DoF	More than the minimum
Repeatability	Very high	High if machining and preload are good
Stiffness	Usually lower	Very high
Load capacity	Limited by contact stress	Good, load is distributed
Sensitivity to manufacturing error	Little assembly stress	Requires small errors or suitable elasticity
Applications	Optics, metrology, precision modules	Indexing tables, machine tool couplings, heavy fixtures

5. Over-constraint: design error or deliberate engineering?

Over-constraint occurs when the same degree of freedom is locked by several independent elements. The classic example is two close-fitting round pins in two close-fitting round holes. The centre distance between the two holes cannot be identical on both parts, so the system easily jams or is forced into deformation during assembly.

Over-constraint is not always wrong. It is used deliberately in multi-tooth couplings, large mounting faces and systems with many rest pads. But at least one of the following conditions has to hold:

The surfaces are machined together to high accuracy.
An elastic element absorbs the error.
A self-aligning or self-equalizing mechanism exists.
The clamping force is evenly distributed.
The tolerance chain has been analysed.

Without these conditions, over-constraint generally leads to three problems: difficult assembly, deformation after assembly and unstable repeatability.

6. The locating datum has to come from function

A good datum is not necessarily the largest face or the easiest one to rest on. It should be chosen from the surface that directly determines the function of the assembly.

For example:

For a shaft and bearing assembly, the important datums are the working axis and the axial shoulder.
For a mould, the datum has to relate to the parting line and the cavity position.
For a drill fixture, the datum has to relate directly to the drawing dimension from the hole to the functional face.
For an inspection camera, the mechanical datum has to relate to the field of view, focal length and optical axis, not merely to the machine frame.

6.1 Design, machining and inspection datums should coincide where possible

Every datum transfer adds error. If a part is designed from face A, machined from face B and measured from face C, the error chain is far harder to control than when a single datum system is used throughout.

In practice they cannot always coincide. Where a datum transfer is unavoidable, show it explicitly with a dimensional chain diagram and put the transfer error into the total error budget.

7. The Abbe principle and offset-induced error

The Abbe principle requires the measuring scale or measurement line to lie along the same line of action as the dimension being controlled. When the sensor sits an offset h away from the working point, a small angular error θ produces a linear error:

e ≈ h × θ

Where:

e: positional error at the working point.
h: offset between the measurement line and the working point.
θ: angular error in radians.

For example, an encoder is mounted 200 mm below the tool tip. If the slide has a pitch error of 0.01°, roughly 0.0001745 rad, the error at the tool tip is approximately:

e ≈ 200 × 0.0001745 = 0.0349 mm

An encoder with 1 µm resolution does nothing to remove this ~35 µm error. The problem lies in the mechanical arrangement, not in sensor resolution.

Measures to reduce Abbe error:

Place the linear scale or encoder near the line of action of the load.
Use two symmetrically placed scales and average them when angular control is needed.
Increase the pitch and yaw stiffness of the slide.
Bring the working point closer to the guideway plane.
Measure and compensate the angular error if the layout cannot be changed.

8. The Bryan principle and angular error during motion

In precision motion systems, not only linear position but also the pitch, yaw and roll of the slide affect the working point. The Bryan principle emphasizes measuring and controlling these angular motions in the machine coordinate system.

A slide can report the correct position at the encoder while the probe, tool head or camera sitting far from the guideway plane is still displaced because the table is tilted. On machines with long travel, changing loads or a high centre of gravity, this error is usually larger than first expected.

High-accuracy design has to consider:

Pitch, yaw and roll over the full travel.
Guideway straightness in both directions.
Stiffness of the table and frame under changing load.
Encoder position relative to the load centre.
Error compensation with a calibration map where mechanics cannot eliminate it entirely.

9. Accuracy and repeatability are different concepts

A mechanism can repeat very well and still sit consistently away from the nominal position. Conversely, one can have the correct mean while scattering widely on each return.

Absolute accuracy: closeness to the nominal position.
Repeatability: scatter when the same action is performed many times.
Resolution: the smallest step a sensor or mechanism can detect or command.

In quick-change jigs or pallets, repeatability usually matters more than absolute accuracy because a fixed error can be calibrated out. In assemblies where several parts interact directly, absolute accuracy matters a great deal because you cannot compensate each sub-assembly after the fact.

When reading a catalogue, do not treat these three figures as interchangeable.

10. Round pin and diamond pin: the standard configuration for joining two parts

Dowel pins usually work alongside bolts. The pins define the position; the bolts create clamping force and keep the assembly against the mounting face.

10.1 Why not two close-fitting round pins?

Suppose the nominal centre distance between two pins is L. Each part has a centre-distance tolerance, a hole diameter tolerance and a positional tolerance. When both pins lock in X and Y, the system has nowhere left to absorb error.

Common results:

It only assembles with a hammer or heavy force.
After the bolts are tightened, the part is pulled out of position.
Pins or holes wear quickly after a few assembly cycles.
The same drawing produces some assemblies that fit and some that do not.

10.2 One round pin and one diamond pin

The round pin locks two directions in the plane. The diamond pin locks only the direction needed to prevent rotation, while the direction along the line between the two pins is released to absorb centre-distance error.

When using a diamond pin, note:

The narrow section of the pin must be oriented along the direction to be released.
If the pin is pressed into the base, provide anti-rotation or mark the fitting orientation.
Working surfaces should be hardened and ground where assembly is frequent.
Provide a lead-in chamfer to avoid chipping the hole edge.
Provide a pin extraction position or a threaded puller hole for maintenance.

10.3 One round hole and one slotted hole

You can keep two round pins and make the second hole a slot instead. This is easy to understand, needs no special pin and absorbs error in one direction.

Disadvantages:

Machining a slot can take longer than reaming a round hole.
If the slot is too large, rotational control is reduced.
The slot direction and dimensional tolerance have to be stated clearly on the drawing.

10.4 Pin spacing directly affects angular error

With an equivalent clearance Δ and pin spacing L, the small angular error can be estimated as:

θ ≈ Δ / L

Increasing the pin spacing reduces angular error. However, do not place pins too close to a thin edge, near a deformation zone or where the temperature differential is large.

11. Locating bosses on castings and plastics

A boss is a cylindrical feature moulded or cast integrally with the part and fitted into a hole in the mating part. It is a very effective way of reducing component count in:

Injection-moulded parts.
Pressure die castings.
Equipment housings.
High-volume assemblies.

Boss design has to consider all of the following together:

Material shrinkage.
Draft angle for mould release.
Roundness and concentricity after forming.
Deformability of the boss wall.
Assembly clearance over the working temperature range.
Risk of cracking at the boss root when a screw is tightened.

A locating boss and a screw boss should not automatically be treated as the same feature. If a self-tapping screw deforms the boss, the relative position can change. Where higher accuracy is needed, separate the locating boss from the boss that carries the tightening load.

12. Splines and serrations: transmitting torque while locating angularly

A spline uses many axial teeth to transmit torque between a shaft and a hub. Compared with a single key, the load is shared across many teeth, so torque capacity is higher and concentricity is usually better.

Two common groups:

Splines: relatively large teeth, and can allow axial sliding while still transmitting torque.
Serrations: smaller, denser teeth, suited to fixing an angle with low backlash.

When using a spline or serration as a locating element, control:

The centring method — major diameter, minor diameter or tooth flank.
Rotational backlash.
Concentricity between the spline and the functional journals.
Engagement length and load distribution across the teeth.
Lubrication, fretting protection and heat treatment.
The possibility of assembling at the wrong angle if the tooth count is symmetric.

13. The hole–shaft fit decides the function after assembly

A fit is not merely a tolerance symbol on a drawing. It decides whether the part can slide, rotate, be removed, or is held permanently after assembly.

Fit type	State	Typical application	Points to note
Clearance fit	Clearance always present	Sliding shafts, guide bushings, frequently removed parts	Clearance creates play and positional error
Transition fit	Can be slightly clear or slightly interference	Removable dowel pins, hubs needing concentricity	Assembly difficulty depends on the actual tolerance distribution
Interference fit	Interference present	Fixing bushings, bearing rings, permanent pins	Generates stress; press force and thin-wall strength must be calculated

When choosing a fit, determine:

Which part is the replaceable one.
How often it is assembled and disassembled.
Assembly temperature and operating temperature.
Whether the two materials have different expansion coefficients.
Radial load, axial load and torque.
The machining method that achieves the tolerance.
Whether the shop can measure it.

Do not choose a tolerance simply because "we have always used this". A fit that suits steel on steel can become far too tight when one side is aluminium and the temperature swings widely.

14. Fixtures: separate locating from clamping clearly

A fixture turns a skill-dependent operation into a repeatable process. On the shop floor, "jig" is used loosely for many kinds of workholding, but functionally they can be distinguished:

Jig: locates the part and guides the tool, for example with a drill bushing.
Fixture: holds and locates the part, but does not guide the cutter directly.

With CNC machines the control system handles tool guidance, so most modern workholding is essentially a fixture.

14.1 Clamping force must act towards the datums

A correctly conceived fixture has a clear load path:

Clamping element → part → rest point → fixture body → machine table

If the clamping force is offset from the rest point, the part can bend. If it pushes the part away from a side locator, the position depends on friction rather than on the datum.

Layout rules:

Clamp near the rest points and near the cutting-force zone.
Avoid clamping between two widely spaced supports on a thin part.
Do not route clamping force through a region prone to deformation.
The main cutting force should push the part onto the datums rather than pull it off.
With pneumatics or hydraulics, add a sensor confirming the clamped position.

15. Machine vices and workpiece lift

A vice is the basic fixture for milling and drilling. However, simply putting the workpiece in a vice and tightening it does not guarantee the workpiece sits flat on the base.

As the movable jaw advances, friction at the jaw face can produce an upward force component, lifting the workpiece off the parallels. A lift of a few hundredths of a millimetre is enough to affect parallelism and depth of cut.

Precision vices usually have an anti-lift mechanism that converts part of the tightening force into a downward pull on the movable jaw. When selecting and using one, check:

Parallelism of the base and jaw faces.
Whether the anti-lift mechanism actually works.
Whether the parallels are clean and the same height.
Whether the jaw faces are dished, worn or holding chips.
Whether the tightening force suits the stiffness of the workpiece.

Soft or thin-walled workpieces should use soft jaws machined to the part profile rather than more clamping force.

16. Chucks and collets in turning

16.1 Three-jaw self-centring chuck

The three jaws move together, so parts change quickly and it suits general production. Repeatability depends on the condition of the scroll and jaws, cleanliness and the clamping position on the jaws.

Do not assume a three-jaw chuck always returns the part to the exact centre after removal. Where several surfaces need high concentricity, machine them in one setup or use soft jaws bored in place.

16.2 Four-jaw independent chuck

Each jaw is adjusted separately, which suits:

Square or asymmetric blanks.
Parts that must be held off-centre.
Work that requires dial-indicator centring.

The drawbacks are longer setup time and dependence on operator skill.

16.3 Collet chuck

A collet grips around the workpiece circumference through elastic deformation. The large contact area gives:

Good concentricity.
Little marking of the workpiece.
Stable repeatability.
Suitability for small bar work and continuous production.

A collet only works well within its designed diameter range. Forcing a collet onto a workpiece that is too small or too large gives uneven contact, reduces grip and increases runout.

17. Locating in moulds: guide pins and interlocks

17.1 Guide pins and guide bushings

Guide pins bring the two mould halves together from a not-quite-concentric state to a position close to fully closed. The pins are usually hardened and work with a replaceable bushing.

Factors to control:

Pin-to-bushing clearance.
Guide length before other mould components begin to engage.
Pin hardness and bending resistance.
Lubrication and grease grooves.
Bushing replaceability as it wears.
Avoiding a situation where the guide pins carry the entire lateral force when the mould closes.

17.2 Interlocks hold the final position

An interlock uses tapered faces or square blocks that engage near the end of the closing stroke. It provides higher lateral stiffness than a guide pin and resists mould shift under injection pressure or stamping force.

Guide pins are mainly for guidance. Interlocks are responsible for locking the final position. Using guide pins in place of interlocks in a mould with high lateral force wears the pins and bushings quickly, increasing flash and cavity misalignment.

18. V-blocks for round parts

A V-block locates a shaft or tube along two contact lines on the V faces. This prevents rolling and establishes the centre from the geometry of the groove.

Applications:

Measuring runout with a dial indicator.
Drilling cross holes in a shaft.
Marking out round parts.
Inspection setups for diameter and straightness.

Long shafts usually use two V-blocks. Both must have the same reference height and sit on the same plane. V-angle error, wear along the contact lines or dust under a block all shift the shaft centre.

For precision measurement:

Use hardened and ground V-blocks.
Keep the measuring set separate from the rough machining set.
Check wear periodically with a master bar.
Do not drag a burred shaft across the V faces.

19. Zero-point systems for fast jig and pallet changes

A zero-point system combines locating and clamping of a pallet through pull studs or nipples fitted to the pallet, engaging with clamping modules on the machine table.

A complete system usually assigns distinct roles to the studs:

A datum stud establishing the X–Y position.
A diamond stud controlling rotation while releasing centre-distance error.
Clamping studs providing only the pull-down force, taking no part in lateral locating.

That role split is essentially the 3-2-1 principle applied to a quick-change system.

Many commercial systems quote repeatability around 5 µm or better depending on series, size, load and cleanliness. The catalogue figure is only achieved when:

The mounting face is machined to requirement.
No chips sit on the module contact face.
Air or hydraulic pressure is adequate.
The pallet is stiff enough.
The pull studs are not worn.
A periodic inspection routine is followed.

Zero-point systems suit high-mix production, automated pallets, robot cells and machines that need less downtime for fixture changes. The initial investment is high but can be offset by reduced setup time and the ability to standardize pallets across several machines.

20. Specialized locating solutions

20.1 Magnetic clamping

Magnetic clamping holds a steel mould or workpiece with electromagnets or switchable permanent magnets. The advantages are an unobstructed working surface, no protruding clamp arms and fast mould changes.

Points that must be assessed:

Whether the material is sufficiently ferromagnetic.
Thickness and flatness of the contact surface.
Holding force in the presence of a gap, paint layer or rust.
Magnetic field effects on nearby sensors and equipment.
The safety mechanism on power loss.
Sensors confirming the magnetization state and holding force.

Do not rely on the nominal holding force in a catalogue. Actual force drops sharply when the surface is not flat or the contact area is insufficient.

20.2 Expanding or contracting locating pins

An expanding pin provides generous clearance while the part is loaded, then expands to eliminate play against the hole. This suits robots because it reduces the risk of jamming during loading while still giving high repeatability once locked.

When applying it, consider:

The permitted hole diameter range.
Air pressure and the state on loss of air.
Lateral load capacity.
Service life of the expanding mechanism.
Cleanliness of the workpiece hole.
A sensor confirming the part is fully seated on the datum before the pin expands.

An expanding pin should not be used to pull a misplaced part into position. The robot still has to place the part within the mechanism's capture zone.

20.3 Ball plungers for light locating

A ball plunger applies spring force to a ball and suits:

Detent or click mechanisms.
Temporarily holding a cover or lever.
Manually adjusted rotary tables.
Lightly stopping a sliding part.

A ball plunger is not a precision locating element under heavy load. Repeatability depends on the groove profile, spring force, friction and wear. Where an accurate angle must be held, add a rigid pin or a stop face after the detent is selected.

20.4 Common commercial product groups

Manufacturers use different trade names, but they fall into the functional groups below. When comparing, do not look only at a repeatability figure; check load, torque, air supply conditions, mounting orientation, self-cleaning ability and the maintenance interval.

Solution group	Typical makers or product lines	Suits	What to check when selecting
Precision stages and piezo stages	THK Precision and other precision stage makers	Optics, semiconductor, metrology, micro-positioning	Travel, load, stiffness, pitch/yaw/roll, encoder position
Multi-tooth couplings and indexing tables	NIKKEN, IZUSHI and other machine-tool indexing makers	High-load angular positioning, high torsional stiffness	Tooth type, clamping force, angular repeatability, chip resistance
Tapered locators and error-compensating locators	IMAO and other fixture component makers	Pallets, removable plates, fixtures needing less play	Direction of error release, pull-down force, taper surface wear
Pneumatic expanding pins	KOSMEK and other automatic clamping makers	Robot loading, holes with large assembly clearance	Diameter range, state on air loss, lateral load, seating sensor
Zero-point systems	STARK from ROEMHELD-HALDER, Q-Lock from NABEYA and equivalents	Fast pallet changes, automated cells, high product mix	Module count, datum and diamond stud layout, pull force, cleanliness and stack height

Specifications vary considerably between series. The same maker will offer a version optimized for accuracy, one for heavy load and one for welding or chip-heavy environments. The catalogue is only the first step; the assembly drawing, the operating conditions and the maintenance plan decide whether the system actually suits the application.

21. Tolerance analysis for locating mechanisms

Locating cannot be designed from nominal dimensions alone. Every part carries error, and the total depends on how the dimensions link together.

21.1 Worst-case method

Worst case assumes every dimension sits simultaneously at its least favourable limit:

T_total = |T1| + |T2| + ... + |Tn|

Advantages:

Guarantees assembly in every case if the input data is correct.
Suits safety mechanisms, low volumes or requirements that allow no failures.

Disadvantages:

Easily leads to unnecessarily tight tolerances and high cost.
The probability of every dimension being at its worst limit at once is usually very low.

21.2 RSS method

If the errors are independent with stable distributions, estimate with the root sum of squares:

T_RSS = √(T1² + T2² + ... + Tn²)

RSS gives a more realistic result, but it is only trustworthy when:

The production process is capable and stable.
The tolerance data genuinely represents the real distribution.
No systematic error acts in the same direction.
The variables are not strongly dependent on one another.

In volume production, combine RSS with process capability data such as Cp and Cpk, and verify with Monte Carlo simulation where the error chain is complex.

21.3 Do not ignore the errors that are not on the detail drawing

The real error chain also includes:

Flatness and squareness of the datum face.
Clearance between pin and hole.
Deformation from clamping force.
Deflection of the fixture base.
Thermal error.
Paint, plating or anodizing thickness.
Wear after many cycles.
Dust and chips at the rest points.
Assembly error and bolt tightening torque.

Adding up linear dimensional tolerances while ignoring these can produce an analysis that looks good in a spreadsheet but does not describe the real machine.

22. Choosing a method by the accuracy required

The table below is indicative only. Final accuracy still depends on size, load, material, temperature, cycle frequency and machining capability.

Typical requirement	Common method	Conditions for stability
About 0.1 mm and above	Stops, cast bosses, slotted holes, ball plungers	Stiff structure, sensible clearance, simple operation
About 0.02–0.1 mm	Machined datum face plus round/diamond pins, V-blocks, a good vice	Clean datum face, sufficient pin spacing, correct clamping direction
About 0.005–0.02 mm	Ground faces, hardened locators, tapered pins, precision collets, zero-point	Control of temperature, wear, preload and base stiffness
Below about 0.005 mm	Kinematic couplings, precision expanding pins, direct measurement, error compensation	Thermally stable environment, calibrated measurement, specialist materials and surfaces

Do not select a micrometre-class mechanism simply because the catalogue quotes good repeatability. If the mounting face, machine frame, temperature and measuring method are only good to a few tens of micrometres, a high-precision component cannot repair the whole system by itself.

23. Common mistakes in locating design

23.1 Using two round pins to lock the same two directions

The result is difficult assembly, opened-up tolerances or forced fitting. The fix is a round pin combined with a diamond pin or a slot.

23.2 Using bolts as dowel pins

The bolt shank, thread and through hole usually have large clearance and cannot guarantee position. Bolts should create clamping force; pins or datum faces determine the position.

23.3 Clamping before the part is fully seated

When chips, burrs or angular misalignment prevent full seating, the clamp can lock the part in the wrong state. Add a seating sensor, an air check or a two-stage clamping sequence.

23.4 Placing the clamping force far from a support

A thin part bends under clamping and springs back after release, so the machined dimension changes. Move the clamping point near a rest point or add a self-adjusting support.

23.5 Choosing a datum that is easy to machine but functionally irrelevant

The error from the datum face to the functional surface is added at every setup. Prefer the functional datum and try to unify the design, machining, assembly and inspection datums.

23.6 Ignoring thermal expansion

A long aluminium base rigidly fixed to a steel bar at both ends will generate stress or bow when the temperature changes. Fix one end and allow the other to slide along the expansion direction where the function permits.

23.7 Trusting catalogue repeatability while ignoring dust and wear

A single small chip on a locating surface is enough to destroy the advantage of a precision component. Design in self-cleaning ability, air blow, shielding and a maintenance schedule.

24. Maintaining and checking the locating system

Accuracy is not decided only at acceptance. A good locating system must have a way of being checked and restored after wear.

24.1 Periodic inspection items

Clean datum faces, pins and holes before each shift or per the production cycle.
Check for wear marks, scoring, pitting and deformation at the contact points.
Measure repeatability with a master part or master pallet.
Check pneumatic, hydraulic or spring clamping force.
Check the sensors confirming clamp/unclamp and seating.
Check play in guide bushings, chucks, collets and zero-point mechanisms.
Lubricate with the correct product; avoid heavy oils that trap chips on datum faces.
Replace locators at the wear limit rather than waiting for a rejected product.

24.2 Design for maintainability

The drawing should already provide:

Locators as replaceable inserts.
Threaded holes or flats for removing pressed pins.
Chip escape grooves.
Accessible measurement positions.
Reference marks for recalibration.
A wear-parts list and replacement intervals.

A very accurate dowel pin that cannot be removed once worn is poor maintenance design.

25. Safety in automatic locating and clamping mechanisms

For pneumatic, hydraulic, electromagnetic fixtures or automatic pallet changers, locating has to be considered together with the safety function.

Minimum checklist:

What state does the mechanism go to on loss of power or air?
Is there a mechanical lock or spring holding the load?
Is there a sensor confirming the part is on its datums before clamping?
Is the machine allowed to run before all pins and clamps are confirmed?
On unclamping, can the load fall or slide?
Are the manual clamping zone and the pallet motion zone guarded?
Can the sensors detect a partially engaged stud?
Is there a force limit so soft parts are not crushed?

With magnetic clamping, specifically confirm the actual holding force and the state on power loss. With heavy pallets, never rely on a software signal alone; provide mechanical confirmation or an independent sensor.

26. Locating design checklist before releasing the drawing

Function

Have the six degrees of freedom of the part been identified?
Which must be locked and which must remain free?
Does the chosen datum relate directly to the function?
Is absolute accuracy required, or mainly repeatability?

Locating elements

Is anything inadvertently over-constrained?
If two pins are used, is it a round–diamond or round–slot configuration?
Is the spacing between locating points large enough to control angle?
Do pins, holes and rest faces have suitable lead-in chamfers?
Do the locator material and hardness suit the number of cycles?
Is there a risk of marking a soft surface?

Clamping force

Does the clamping force push the part onto its datums?
Are the clamping points close to the supports?
Does the part bend or twist when clamped?
Can cutting force, inertia or gravity lift the part off its datums?
Are auxiliary or self-adjusting supports needed?

Tolerance and temperature

Does the tolerance chain include the pin-to-hole clearance?
Has the angular error from pin spacing been calculated?
Has Abbe error at the working point been checked?
Do the materials have different expansion coefficients?
Do plating, paint or surface treatment change the fitted dimensions?

Manufacturing and maintenance

Can the shop machine and measure the specified tolerances?
Does the datum face have chip grooves or cleaning air?
Can the locators be replaced when worn?
Is there a master for checking repeatability?
Are the assembly, clamping and removal sequences clear?
Does the mechanism prevent reversed or wrongly oriented assembly?

27. Conclusion

A good locating system is not the one with the most pins or the tightest tolerances. It is the one that locks the right degrees of freedom, takes its datums from function, absorbs the manufacturing error it needs to, and holds its repeatability under real production conditions.

Key principles to remember:

Always start from the six degrees of freedom.
Use the 3-2-1 principle to avoid unnecessary redundant locking.
Separate the locating function from the clamping function.
Choose rest points according to the stiffness, flatness and surface condition of the part.
Use a round pin with a diamond pin or a slot when locating on two holes.
Place sensors and measuring points according to the Abbe principle; do not judge accuracy from encoder resolution alone.
Where high stiffness is needed, deliberate over-constraint is acceptable, but machining, preload and elastic deformation have to be controlled.
Bring temperature, clamping force, dust, wear and maintenance into the error chain from the design stage.
Choose a solution from the real requirement of the whole system, not from the best specification of one isolated component.

When these points are handled from the start, fixtures assemble more easily, machines need less adjustment and product quality stays stable through every part change, jig change and maintenance cycle.

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