An eccentric line coupling connects parallel shafts that are laterally out of line using matching faceplates and several pivoted bars. The historical arrangement in Hiscox figures 1301–1302 uses four or five bars with bends to clear one another.
The shafts rotate together while the bars translate around circular paths. Pivot joints allow the bars to move relative to the rotating faceplates. The animation shows the axial gap and bar bends in perspective, plus an end projection that makes the corresponding pin connections visible.
Eccentric Line Coupling Interactive Calculator
Set the shaft offset, axial gap and pin-circle size. Follow five rigid offset bars as the parallel shafts turn together.
Equation Used
- Parallel input and output shaft axes; no angular misalignment.
- Equal pin-circle radii and five corresponding pins at 72° intervals.
- Both plates have the same angular phase and speed.
- Bars are rigid; their end-pin vector stays constant.
- Bend proportions and component thickness are illustration choices.
Hiscox figures 1301–1302: parallel shafts, matching faceplates and pivoted offset bars. All five bars retain their rigid shape.
Two faceplates and five translating bars
The input and output shafts have parallel axes. Their faceplates lie in parallel planes separated by an axial gap. Both plates have the same pin-circle radius and the same five equally spaced pin positions.
Each input pin connects to the corresponding output pin through one rigid bar. In the illustrated assembly both plates have the same angular phase. The vector between every matching pair of pins is therefore constant: the selected lateral shaft offset and axial plate gap.
As the input turns, all five bars move around the pin-circle radius while retaining their orientation and shape. The output plate turns through the same angle in the same direction. The joints rotate relative to the bars; the bends do not flex to create the motion.
Hiscox’s side view shows why depth matters. Bars that appear to overlap in the end view can pass at different axial positions. The illustrated coupling uses the same offset shape for all five bars, with two rigid bends between their end pivots.
Explore the coupling dimensions
Use lateral shaft offset to set the distance between the shaft axes in the end view. Axial gap sets the separation of the faceplate planes along the shaft direction. These are different dimensions, and both contribute to the distance between corresponding pins.
Pin-circle radius sets the size of the circular path followed by every bar. Changing it changes pin speed at a given shaft rpm. Changing input speed changes output speed and the animation’s cycle time.
The end projection deliberately uses unfilled plate outlines to reveal the pin connections. It does not represent all the bars occupying one plane. The perspective view shows their actual axial positions.
Constant pin spacing and one-to-one rotation
Let s be the lateral shaft offset, g the axial faceplate gap and R the common pin-circle radius. For pin j, φⱼ=θ+2πj/5. Its input position is Aⱼ=(R cosφⱼ,R sinφⱼ,0), and its output position is Bⱼ=(s+R cosφⱼ,R sinφⱼ,g).
Thus Bⱼ−Aⱼ=(s,0,g), independent of shaft angle. The distance between the end pivots is √(s²+g²). Corresponding pins on both faceplates have identical velocity vectors, so the bars translate without rotating and the output speed equals the input speed.
For input speed N in rpm, pin speed is 2πRN/60. A full turn takes 60/N seconds. The calculator reports the blue input pin’s instantaneous X and Y coordinates relative to its fixed shaft.
The displayed bar has intermediate points at 12% of s and 25% of g, then 88% of s and 75% of g. Its centerline length is 2√[(0.12s)²+(0.25g)²]+√[(0.76s)²+(0.50g)²]. These bend proportions are an explicit illustration choice; they are not historical manufacturing dimensions.
Example: parallel shafts 150 mm apart
Choose a lateral offset of 150 mm, an axial gap of 120 mm and a pin-circle radius of 50 mm. Matching end pins remain √(150²+120²)=192.09 mm apart throughout the turn.
At 6 rpm both shafts make one revolution every ten seconds. Every pin and bar translates at 31.42 mm/s. At the reset position, the blue input pin is at X=50 mm and Y=0 mm. At a quarter-turn it is at X=0 mm and Y=50 mm.
Geometric scope
This model illustrates the historical coupling principle with five bars. The pin circles match exactly and the shaft axes remain parallel. It does not model angular misalignment, flexible shafts or an adjustable eccentric-bore correction.
Plate thickness, pin sizes, rod diameter and bend proportions are shown to explain the arrangement. The calculator reports geometry and ideal motion, not torque capacity, fatigue life, dynamic balance, friction, bearing loads or a safe operating speed.
The selected range keeps the drawn bars separated. Real equipment needs a detailed three-dimensional clearance and strength design, including the surrounding shafts, guards and bearings.
Eccentric line coupling questions
Do the bars bend during operation?
No. They are rigid offset links. Their bends stay fixed while the bars translate around circular paths.
Are the shaft bores eccentric in their faceplates?
No. The faceplates rotate about their shaft centers. It is the two shaft axes that are laterally out of line.
Why do some bars cross in the end projection?
That view collapses the axial dimension. The perspective view shows how the links occupy different positions in space.
Does increasing shaft offset change output rpm?
No. With matching pin patterns and this assembly phase, the two shafts retain one-to-one rotation. Offset changes the required bar geometry.
Why are five bars used?
The historical description permits four or five. The illustrated coupling uses five equally spaced connections.
Reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, figures 1301–1302, printed page 320: faceplates on parallel out-of-line shafts joined by four or five offset bars, with a side view of the bends. The working dimensions and bar profile are illustrative; they are not manufacturing dimensions.
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