A Canfield joint supports a moving platform on three hinged legs, each with two equal-length links. Three driven base hinges control the platform pose. Explore the connected geometry below.
Canfield Joint Interactive Calculator
Set the three base angles, hinge spacing and link length. The animation cycles between the entered pose and a level reference; result cards always describe your entered pose.
Equation Used
- Equilateral base and platform hinge triangles; identical length for all six links.
- Angles are measured upward from the outward radial direction in the base plane.
- Ideal midplane-symmetric assembly with unrestricted intermediate joints; finite joint limits, collisions, loads and stiffness are not solved.
- Zero-angle combinations can bring the platform into the base plane. These are ideal limiting configurations, not usable clearance predictions.
- Autoplay demonstrates a smooth excursion from the entered angles to 30 degrees and back; it is not a specified motor-speed profile.
The platform is obtained by reflecting the base triangle across the plane through the three intermediate joints. Equal base angles keep the platform level; unequal angles can change both tilt and center position. Results describe this ideal symmetric assembly.
Three legs support one moving platform
Each leg has two equal-length links. A driven hinge connects its lower link to the base; an intermediate joint joins the links; the upper link ends at a platform hinge. The drawing makes all six links and their connections visible.
The selected model assumes midplane symmetry: reflecting the base half across the plane through the three intermediate joints produces the upper half. This construction closes the linkage without stretching a link or moving a base hinge.
Pointing and positioning
A parallel platform can orient a supported instrument while leaving an opening through its center. The purple arrow shows its pointing direction. The center can also translate as the joint moves.
This calculator describes geometry. It does not determine motor torque, payload capacity, pointing accuracy or whether a proposed instrument clears the frame.
Calculate a closed spatial linkage
The three base hinges are spaced 120 degrees apart on a circle of radius b/√3. Each intermediate joint lies one link length L from its base hinge, in that hinge’s radial vertical plane. Its horizontal radial displacement is L cos(a) and its height is L sin(a).
Let n be a unit normal to the plane through the three intermediate joints and q any point on that plane. A base point x reflects to x − 2n[n·(x − q)]. Applying this operation to each base hinge gives the platform hinges; applying it to the base center gives the platform center.
Height is the vertical coordinate of the platform center. Lateral offset is its horizontal distance from the base center. The upward platform normal is obtained by reflecting the downward base normal. Its angle from vertical is the platform tilt.
Check equal and unequal input angles
With all three base angles at 45 degrees and each link 100 mm long, the platform remains level. Its center height is 2 × 100 × sin(45°) = 141.42 mm, with zero lateral offset.
Set all three angles to 30 degrees and the height becomes 100 mm, still with zero tilt. Change just one angle and the intermediate-joint plane tilts, which changes both platform orientation and center position.
Doubling every length leaves the tilt unchanged while doubling all distances. Changing hinge spacing or only the link length alters the proportions and can change the resulting pose.
Geometry and physical limits
The links and hinge spacing remain rigid throughout playback. However, the rendered bars have illustrative thickness; the solver treats them as ideal lines. Extreme poses may intersect or leave insufficient room for bearings and a payload.
Center height and lateral offset describe the ideal platform position. Check bearings, joint stops, bar thickness and payload clearance separately before using a displayed pose in a physical assembly.
Questions about this model
Why do equal angles produce zero tilt?
All three intermediate joints are then at equal height. Their plane is horizontal, so the reflected platform remains parallel to the base.
Why are there six links instead of three?
Each of the three legs contains a lower and an upper link connected at an intermediate joint.
What does the animation cycle represent?
It moves smoothly between your entered pose and the 30-degree level reference. The result cards describe the entered pose, and the drawing shows its current live pose.
Does the calculator check physical joint limits?
No. It solves an ideal symmetric linkage. Real bearings, joint stops, collisions and load capacity require separate analysis.
Primary kinematics reference
Bueno, Collins, Hylton and Short, A Geometric Approach to the Kinematics of the Canfield Joint (2021). Figure 2 establishes the two-link legs and hinge arrangement; Sections II–III describe the midplane-symmetric forward construction used here.
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