An ideal Schmidt coupling uses three angle-synchronous discs and two levels of identical parallel links to transmit rotation at a constant 1:1 ratio between radially offset parallel shafts. For equal selected link radii L and shaft offset E, the center-disc axis is one of the two intersections of circles of radius L about the input and output axes.
Ideal Schmidt Three-Disc Constant-Velocity Topology
Explore source-grounded ideal closure for a three-disc, six-link Schmidt coupling with radially offset parallel shafts.
Equation Used
- Input, center and output disc pin arrays are identical and angle-synchronous.
- The two link levels each use three equal rigid links of selected length L.
- The displayed upper circle intersection is one of two mirror installations.
- Product-specific offset, torque, speed, balance, bearing and life limits are excluded.
The secondary figure uses the same exact equal-link closure and synchronous disc angles.
Three discs and two three-link levels
The input and output shaft axes P and Q are fixed and offset by E. The center-disc axis R is placed so RP = RQ = L. Each disc carries the same equilateral three-pin array, and corresponding pins are joined by three identical links on each side of the center disc.
All three arrays rotate at the same angle. Because corresponding radial pin vectors are equal, every link vector remains equal to RP or RQ and all six rigid link lengths stay constant through the full cycle. The second circle intersection gives the mirror installation.
What the calculator determines
Select ideal input speed, shaft offset and equal link radius. The calculator returns the synchronous output speed, center-axis rise above the shaft-center line, branch angle and offset as a percentage of the full two-link span.
This is ideal topology and closure, not a coupling selector. Real minimum and maximum offset, extended-position exclusion, torque, speed, bearing, balance and life limits are product-specific.
Ideal equal-link closure
nout = nin. With RP = RQ = L and PQ = E, center rise is h = √(L² − E²/4), branch angle is α = cos⁻¹(E/2L), and selected span ratio is 100E/(2L).
The calculator bounds E below 2L, so both equal-link circle intersections exist. It also excludes zero offset because manufacturer guidance requires a nonzero product-specific minimum.
Selected ideal example
At 300 rpm, E = 100 mm and L = 140 mm, ideal output is 300 rpm. The center-disc axis lies about 130.8 mm from the shaft-center line, α is about 69.1°, and E is 35.7% of the full 2L span.
Source boundary
The earlier drawing assigned incompatible independent pin motions and used an arbitrary clearance threshold. The revised model follows the patent's identical three-pin arrays, two groups of identical parallel links and fixed center R defined by RP and RQ.
Manufacturer documentation additionally requires a nonzero minimum offset and excludes an extended position. Exact allowable offsets and ratings must come from the selected coupling size; this normalized model does not infer them.
Questions
Why is the center disc called floating if R is fixed?
It is not supported by a shaft bearing. For fixed P and Q its ideal center R is geometrically defined, while the disc rotates about R.
Do all three discs keep the same angle?
Yes in the ideal Schmidt topology, giving constant-velocity 1:1 transmission.
Can E be zero?
The geometric circles coincide at zero offset and R is not uniquely defined; manufacturer guidance requires a product-specific minimum offset.
Can this select a real coupling?
No. Use the manufacturer's size-specific offset, torque, speed and installation limits.
Primary references
- EP0196859A2, Torque coupling — documents the known Schmidt coupling's three identical triangular pin arrays, identical parallel links, 1:1 synchronized rotation and center R defined by RP and RQ.
- SCHMIDT-KUPPLUNG technical catalog — confirms three discs, two link levels, angle-synchronous transmission, nonzero minimum offset and excluded extended position.
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