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Stewart Platform Design
A Stewart platform is defined by twelve attachment coordinates, the joint type at each end, the actuator stroke range and the neutral height. Those few numbers determine everything the machine can and cannot do. This guide explains how each choice is made and what it costs elsewhere in the design.
This is a mechanical design guide — geometry, topology, joints and workspace analysis. It does not list platform models, payload ranges or specifications. Looking to configure or specify a platform for a project instead?
12 coordinates
Six base points and six platform points define the kinematics entirely.
No optimal geometry
Every dimension is a coupled trade-off, not a value to maximise.
6-dimensional workspace
An envelope mapped by sampling, never a box of per-axis maxima.
Joints set fatigue life
Alternating load at the joints governs, not peak static load.
What a Stewart Platform Design Must Solve
Designing a Stewart platform is not a matter of picking six actuators and two plates. It is the problem of finding one geometry that simultaneously satisfies four requirements that pull against each other — and doing so with margin, because none of them can be adjusted independently after fabrication.
Direct answer. A Stewart platform design is fully specified by twelve attachment coordinates, the joint type at each end of each limb, the actuator stroke range and the neutral height. Every performance characteristic — workspace shape, stiffness, force capability, natural frequency, singularity margin — is a consequence of those choices rather than something specified separately.
Reach the Required Motion
The complete commanded trajectory, including combined translation and rotation, must fit inside the workspace with margin — not just the individual axis extremes.
Carry the Load
The structure, joints and actuators must handle the moving assembly through the full dynamic envelope, including the alternating loads that determine fatigue life.
Stay Controllable
Force transmission must remain adequate throughout the workspace. A pose that is geometrically reachable but near-singular is not usable.
Be Buildable and Serviceable
Joints must be packageable, structures manufacturable, cables routable and components reachable for maintenance without dismantling the machine.
Anatomy: The Numbers That Define the Mechanism
A complete Stewart platform kinematic definition is surprisingly small. Twelve points in space, a joint type, a stroke range and a nominal height. Everything a control system needs, and everything a competitor would need to replicate the machine, is contained in that list.
The reason the definition is so compact is that a parallel mechanism has no intermediate links. Each limb runs directly from a base point to a platform point, so once those points and the limb lengths are known, the pose is fully constrained. There is no chain of joint angles to accumulate.
This compactness cuts both ways. It makes the kinematics tractable and the calibration well-posed. It also means there is nowhere to hide a mistake — a poorly chosen attachment radius cannot be compensated later by a better controller, because the geometry is the machine.
In practice the twelve coordinates are rarely arbitrary. Most designs place points in three pairs on each plate, with the pairs rotated relative to each other, because that arrangement gives a reasonably symmetric workspace and keeps the worst singularities away from the neutral pose.
B₁–B₆
Base attachment coordinates
Six points on the fixed frame, defined in the base coordinate system. Their radius and pair spacing set limb inclination and force transmission.
Joint type
Cardan or spherical, each end
Determines the constraint each limb applies and the articulation range available before the joint becomes the limiting factor.
h₀
Neutral height
Platform elevation at the nominal pose. Sets how stroke is divided between extension and retraction, and strongly affects lateral stiffness.
P₁–P₆
Platform attachment coordinates
Six points on the moving frame, defined in the platform coordinate system. They set the moment arm through which the limbs control orientation.
Lmin–Lmax
Actuator stroke range
The permitted change in each limb length. Not the same thing as platform travel, and never interchangeable with it.
How Attachment-Point Geometry Changes Platform Behaviour
Base radius, platform radius, paired-point spacing, angular phase and neutral height together set the direction of every limb. Limb direction is what relates actuator extension to platform motion, and actuator force to platform load. Change one dimension and both relationships change everywhere in the workspace.
| Design variable | What it directly changes | What must be checked alongside it | Common unsafe shortcut |
|---|---|---|---|
| Base attachment radius | Limb inclination, base footprint, force transmission ratio. | Joint angle range, foundation interface, interference, actuator load, service access. | Assuming a wider base always gives a larger or stiffer workspace. |
| Platform attachment radius | Upper limb direction, payload interface, moment transfer to the plate. | Top-plate stiffness, payload mounting pattern, rotation envelope, clearance, moving mass. | Minimising the top plate without checking the real payload interface. |
| Paired-point angle | Local geometry at each attachment pair, mechanism conditioning. | Joint packaging, local structure, force distribution, singularity margin. | Copying an angle from a published diagram without its original design conditions. |
| Angular phase | Relationship between base and platform attachment patterns. | Limb crossing, collision, workspace shape, yaw capability, access. | Treating the two plates as independent bolt circles. |
| Neutral height | Nominal limb length, stroke split, platform elevation. | Buckling margin, lateral stiffness, loading or boarding height, facility ceiling, service access. | Adding height to gain heave without recomputing the whole mechanism. |
| Actuator stroke | Permitted change in individual limb length. | Resulting platform pose, joint angles, collision, speed, force, thermal duty, safety margin. | Publishing actuator stroke as if it were platform travel. |
| Commanded pivot point | Translation required to produce a commanded rotation. | Payload clearance, workspace consumption, test objective, measurement reference point. | Moving the pivot in software without rechecking the trajectory. |
There is no universally best geometry. A Stewart platform is not improved by maximising every dimension — the variables trade against each other, so a gain on one axis is paid for on another. A good geometry is one that preserves a specific required trajectory, force transmission, controllability, structural behaviour, manufacturability and service access, each with explicit margin. Any design presented as optimal without stating the application it was optimised for should be treated with suspicion.
3-3, 6-3 and 6-6: What the Topology Labels Mean
Technical literature groups Stewart platforms by how attachment points are arranged. The first number counts distinct locations on the base, the second on the moving platform. The labels are useful shorthand for discussing layout, but they define far less than they appear to.
Topology reference
3-3 Grouping
Three effective attachment locations on each plate, with limbs meeting in pairs at each. Conceptually compact and common in textbooks.
- Two limbs converge at each point
- Joint packaging at the convergence is the hard part
- Rarely built at industrial scale in this pure form
Topology reference
6-3 Grouping
Six distinct base locations connecting to three grouped platform locations. The octahedral arrangement — pairs rotated relative to each other — is the classic industrial form.
- Reasonably symmetric workspace
- Keeps worst singularities away from neutral
- Grouped upper load paths need explicit review
Topology reference
6-6 Grouping
Six independent attachment coordinates on each plate. Maximum freedom in placing points, at the cost of more parameters to justify.
- Each point positioned independently
- Flexible local joint packaging
- Symmetric appearance can still hide unequal spacing
Joint Selection: Spherical or Cardan
Nearly every published description of a Stewart platform assumes spherical joints at both ends of each limb. That is the textbook form and it keeps the mathematics clean. It is not the only option, and for a motion base carrying substantial payload through millions of cycles it is often not the right one.
The difference comes down to one rotational degree of freedom. A spherical joint permits rotation about all three axes, including about the limb’s own axis. A Cardan (universal) joint permits only two, constraining that axial spin.
That single constraint changes the load path. With spherical joints at both ends, each limb is a two-force member that cannot resist torsion — elegant to model, but it means any torsional load must be carried entirely by the arrangement of the six limbs together. With Cardan joints, each limb resists torsion about its own axis, and the load path through the mechanism becomes determinate.
For a precision positioning hexapod moving a few kilograms over micrometres, the spherical form is usually preferable — the free articulation maximises workspace and the loads are small. For a motion base carrying a cabin or test article through high accelerations, the alternating loads at each joint govern fatigue life, and the stiffness advantage of the Cardan joint matters more than the articulation range it costs.
CSCMotion platforms use Cardan joints. Combined with the prismatic and rotational freedom of the piston inside the cylinder barrel, each limb forms a T-P-S kinematic chain — the origin of the 6-TPS designation used throughout our engineering documentation.
Textbook form
Spherical (ball) joint
Three rotational degrees of freedom at each end. The limb becomes a pure two-force member.
| Rotational DOF | 3, including free spin about the limb axis |
| Torsion | Cannot be resisted by the limb |
| Articulation | Large — rarely the workspace limit |
| Best suited to | Precision positioning, light payload, small envelope |
Used in CSCMotion platforms
Cardan (universal) joint
Two rotational degrees of freedom. Axial rotation is constrained, giving a determinate load path.
| Rotational DOF | 2, axial rotation constrained |
| Torsion | Resisted by the limb itself |
| Articulation | Restricted — must be checked at every pose |
| Best suited to | High-payload motion bases under alternating load |
Design consequence: choosing Cardan joints moves the workspace constraint. With spherical joints the limiting factor is usually stroke; with Cardan joints, joint articulation frequently becomes the binding constraint before stroke runs out. The workspace analysis must therefore check joint angles at every sampled pose, not only limb lengths. See How a 6DOF Motion Platform Works for how this affects the control model.
From Motion Requirements to a Usable Workspace
A Stewart platform workspace is a coupled six-dimensional region of positions and orientations. It cannot be described as a rectangular box built from maximum X, Y, Z, roll, pitch and yaw values, because using stroke on one axis removes it from the others.
Layer 01
Reachable Workspace
Poses where the kinematic model returns limb lengths inside the stroke range and joint angles inside their permitted articulation. The largest of the three volumes, and the least meaningful on its own.
Layer 02
Collision-Free Workspace
The subset of reachable poses where limbs, joints, platform, base, payload, cabling and surrounding equipment all remain clear of each other. Always smaller, sometimes dramatically so once a real payload envelope is included.
Layer 03
Usable Workspace
The subset that also satisfies actuator force and velocity limits at the required accelerations, maintains acceptable force transmission away from singular configurations, and retains safety margin. This is the only volume worth quoting.
Why the workspace is sampled, not derived
There is no closed-form expression for the boundary of a six-dimensional coupled workspace under all these constraints simultaneously. The practical method is numerical: generate a large set of candidate poses across the region of interest and test each one against every constraint in turn.
CSCMotion uses Monte Carlo sampling to map the reachable envelope, then applies the collision and force constraints to the surviving set. The output is a point cloud describing the usable volume — which can then be checked directly against the customer’s required trajectory rather than against a set of axis maxima that describe six separate poses.
Sizing the Actuator and the Structure
Actuator selection and structural design are not independent activities. The force the actuator must deliver is an output of the dynamic analysis, and it becomes the input load case for the structural analysis. Running them in the wrong order — or in parallel with assumed numbers — is how platforms end up either overweight or underrated.
Define the Moving Assembly
Total mass, centre of gravity and inertia of everything the platform carries: payload, fixture, cabin, occupants, cabling.
Run Multibody Dynamics
Solve the mechanism through the required trajectory to find the peak force each limb must deliver, and where in the workspace it occurs.
Select the Actuator
Choose stroke, force, velocity and duty rating against that peak, with margin for the dynamic condition rather than the static load.
Analyse the Structure
Apply the same peak forces as the load case for finite element analysis of frames and joints, checking static strength and fatigue under alternating load.
The most common sizing error: selecting actuators from the static payload weight. A platform holding two tonnes at rest and a platform accelerating two tonnes at 0.6 g are entirely different machines. Peak limb force in a dynamic manoeuvre routinely exceeds the static share by a large factor, and it does not occur at the pose most people would guess.
A Practical Stewart Platform Design Workflow
The sequence below is the one we follow. Its value is not that any step is unusual, but that each step produces the input the next step needs — so skipping ahead means guessing at a number that a later analysis will contradict.
01 · Establish the Motion Requirement
Define the physical job: what must be reproduced, tested or moved. Capture the complete moving assembly and at least one representative combined trajectory — not a list of per-axis extremes.
02 · Propose a Candidate Geometry
Choose topology, attachment radii, pair spacing, angular phase and neutral height. This is an informed starting point, not an answer — it will be revised.
03 · Map and Test the Workspace
Sample the envelope, apply length, joint-angle, collision and conditioning constraints, then check whether the required trajectory fits inside the usable volume with margin. If it does not, return to step 02.
04 · Solve the Dynamics
Run the trajectory through the mechanism with the real mass properties to find peak limb forces, velocities and where they occur.
05 · Size Actuators and Analyse Structure
Select cylinders against the dynamic peak, then apply those forces as the load case for finite element analysis of frames and joints, including fatigue under alternating load.
06 · Cross-Validate the Dynamic Model
Compute natural frequencies at representative poses on two independent solvers — finite element and multibody. Agreement is the condition for release; disagreement means the model is wrong and must be resolved before fabrication.
07 · Calibrate and Measure the Built Machine
Identify the as-built geometry, compensate it in the controller, then measure positioning accuracy and repeatability on the assembled platform under the agreed test load.
Note the loop between steps 02 and 03. It is normal to iterate several times before a geometry passes. A design that satisfies the workspace requirement on the first attempt usually means the requirement was loose, not that the geometry was inspired.
Common Stewart Platform Design Mistakes
These appear repeatedly in specifications, tender documents and early-stage designs. Each begins with a reasonable idea applied without the condition that makes it valid.
Mistake 01
Treating stroke as travel
Why it fails: platform motion is a geometric consequence of all six limb lengths together. Actuator stroke is an input to that calculation, never a statement of what the platform will do.
Mistake 02
Adding per-axis maxima
Why it fails: each published maximum is measured with the other axes near neutral. Combining them describes a pose that does not exist in the usable workspace.
Mistake 03
Sizing from static payload
Why it fails: peak limb force in a dynamic manoeuvre far exceeds the static share, and it occurs at a pose that is rarely the obvious one. Static sizing produces an under-rated machine.
Mistake 04
Copying a published geometry
Why it fails: a geometry is optimal only for the payload, trajectory and constraints it was designed against. Transplanted to a different application it carries no guarantee at all.
Mistake 05
Ignoring joint articulation
Why it fails: especially with Cardan joints, articulation frequently becomes the binding workspace constraint before stroke does. A workspace check on limb length alone will overstate the envelope.
Mistake 06
Scaling up for more motion
Why it fails: a larger platform has more moving mass and inertia, which raises required force and lowers natural frequencies. With the same actuators it performs worse, not better.
Selected technical references
- Science China Technological Sciences — Theory and methodology for kinematic design of Gough–Stewart platforms
- NIST — Workspace variation of a hexapod machine tool
- Machines (MDPI) — Kinematic and workspace analysis of parallel manipulators
Stewart Platform Design FAQ
Short answers to the design questions engineers ask most often.
What defines a Stewart platform design?
Twelve attachment coordinates — six on the base and six on the moving platform — together with the joint type at each end, the actuator stroke range and the neutral height. Those numbers fully determine the kinematics. Everything else in the design, from structural sizing to control tuning, follows from them.
Is there a best Stewart platform geometry?
No. Geometry is a set of coupled trade-offs, not an optimisation with a single answer. Widening the base improves tilt stiffness but consumes floor space and can reduce rotation range. Raising the neutral height increases heave but worsens lateral stiffness and buckling margin. A good geometry preserves the required combined trajectory, force transmission and structural margin for one specific application.
What do 3-3, 6-3 and 6-6 mean in Stewart platform design?
They describe how attachment points are grouped: the first number is distinct locations on the base, the second on the moving platform. A 6-6 layout has six separate points on each plate; a 6-3 groups the upper attachments into three pairs. The labels describe topology only — they do not define coordinates, joint type, actuator orientation or performance.
Should a Stewart platform use spherical or Cardan joints?
It depends on the load case. Spherical joints allow free rotation about the limb axis, which keeps the mathematics simple but leaves the limb unable to resist torsion. Cardan (universal) joints constrain that rotation, producing a determinate load path and higher stiffness under alternating load — the condition that governs fatigue life in a motion base. The trade-off is a more restricted articulation range that must be checked at every pose.
How is Stewart platform workspace calculated?
By sampling. Because the workspace is a coupled six-dimensional region rather than a box, it is mapped numerically — commonly by Monte Carlo sampling across candidate poses, checking each against limb length limits, joint articulation, mechanical clearance, actuator force and velocity, and conditioning. The result is an envelope, not a list of per-axis maxima.
Why can I not add the maximum values from a specification table?
Each figure is measured with the other axes near neutral. Because all six limbs contribute to every degree of freedom, using stroke on one axis removes it from the others. Maximum surge, maximum heave and maximum pitch describe three separate poses, not one combined pose the platform can reach.
How is a Stewart platform design verified before manufacture?
Kinematic checks confirm the required trajectory fits inside the usable workspace with margin. Multibody dynamics returns the peak actuator force, which becomes the load case for finite element analysis of the structure and joints. Modal analysis is run on two independent solvers so results can be cross-checked. Only after those agree does fabrication start.
Does a bigger platform always give more motion?
No. Scaling up increases moving mass and inertia, which raises the actuator force needed for the same acceleration and lowers the structure's natural frequencies. A larger platform with the same actuators will move less capably, not more. Size is an output of the payload and trajectory requirement, never an input chosen for its own sake.
From Design Principle to Platform Engineering
This guide owns the mechanical design logic. Use the pages below for the working principle, a platform configuration, a custom engineering scope, or how we run the analysis.
Product bridge
Stewart Platform
Platform scope, configuration inputs and the route to an engineering proposal. This is where a commercial Stewart platform enquiry belongs.
Working principle
How a 6DOF Platform Works
Command to measured motion: inverse kinematics, actuator coupling, the forward problem and closed-loop control.
Custom scope
Custom & OEM Platforms
How a bespoke geometry becomes a delivered subsystem: engineering scope, milestones and responsibility split.
Engineering method
Technology Overview
The six analyses behind every platform we ship, from mechanism derivation through modal cross-validation to laser measurement.
From geometry to a real machine
Start With the Assembly and the Motion It Must Produce
Geometry cannot be chosen in the abstract. Send the moving assembly and one representative combined trajectory, and our engineers will tell you what the geometry has to satisfy — and which of your requirements are pulling against each other before anyone commits to a layout.
What a geometry review needs
The inputs that let us evaluate whether a candidate geometry can work:
Complete moving assembly
Total mass and centre of gravity
Inertia, where available
Required translations and rotations
Reference point for those values
Representative combined trajectory
Acceleration and duty cycle
Site envelope and ceiling height