The Schatz linkage is a spatial closed chain with six revolute joints. Its connected bars move in three dimensions while the base stays fixed. Explore its ideal motion and calculate cycle timing and the ratio of an entered length deviation to the reference length.
Schatz Linkage Motion and Cycle Timing
Explore connected spatial motion alongside selected cycle timing and relative entered length deviation.
Equation Used
- One selected input revolution is treated as one selected timing cycle.
- Input speed is constant.
- Relative deviation is only entered ΔL divided by entered L.
- The animation uses ideal geometry; loads, solid-body collisions and dynamics are excluded.
The entered length deviation does not deform the ideal linkage.
Connected six-joint motion
The animation shows the open-type Schatz arrangement: three equal moving bars, two end shafts and a fixed base. Silver barrels show the revolute joints and their directions.
Joint angles follow the closed-form solution in the cited study. The view automatically fits the linkage, so changing reference length scales the physical dimensions while preserving its proportions.
What the calculator determines
Select nominal input revolutions, input speed, reference link length and an entered length deviation. Outputs are selected cycles, seconds per selected cycle, selected run time and relative deviation 100ΔL/L.
The numeric outputs do not include joint angles, closure residual, torque, load or mixing performance. Link motion is calculated separately for the illustration.
Selected timing and relative deviation
Cycles = N, time per selected cycle = 60/n, run time = 60N/n, and relative entered deviation = 100ΔL/L.
Calling the last value a closure error would imply a solved loop-closure model; it is only the ratio of two entered lengths.
Selected-input arithmetic
At one selected cycle and 60 rpm, selected run time is one second. For L = 100 mm and ΔL = 0.5 mm, relative entered deviation is 0.5%.
Technical reference
Analysis and Synthesis of Schatz Six-Revolute Mechanisms, JSME International Journal, 43(1), 2000, pp. 80–91. The illustration uses the open-type dimensions and displacement equations.
Model dimensions and limits
The three equal bars have length L, the fixed base is √3L, and the end offsets are 0.4L. Hinges are ideal revolute pairs. The selected speed controls playback; selected cycle count controls only the run-time calculation.
The model explains rigid-link motion. It does not select bearings, check solid-part clearances or predict mixer performance.
Questions
Does the animation show connected linkage motion?
Yes. The six joint angles follow an ideal closed-form displacement solution.
Is one input revolution proven to produce one figure-eight?
No particular figure-eight path is claimed. The cycle count is a selected input timing convention.
Is relative ΔL a closure residual?
No.
Can this design a Schatz linkage?
No.
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