Brown’s movements 176 and 177 show two settings of one slotted-ring engine coupling. In form 1 the wrist pin bears against the radial slot wall and carries the output crank around. Turning the ring a quarter-turn puts its slot across the pin’s passage, allowing the input pin to pass while the output stays still. This page illustrates form 1 with a dimensioned geometric model.
Slotted-ring Coupling · Engaged Geometry Calculator
Adjust crank radius, pin size and slot opening. Inspect the actual contact or passage in the enlarged detail.
Equation Used
- Rigid planar crank geometry; input and output shafts are coaxial.
- Pin is circular; ring outer radius is selected as 1.5 pin diameters.
- Engaged motion starts after backlash has been taken up.
- Disengaged output is held at rest; the wrist passes through the tangential slot.
- The passage formula is a sufficient clearance bound, not an optimized minimum.
- No material strength, contact stress, friction or impact calculation.
Historical principle after Brown 176/177. Initial impact, axial retaining hardware and switching under power are not modeled.
Two ring settings, two distinct behaviors
A wrist pin fixed to the input crank enters a slotted ring carried by the output crank. With the slot running along the output crank, the pin pushes on a side wall and transmits motion after any clearance is taken up. With the slot turned 90°, the pin can pass through the opening and leave the output behind.
The model uses coaxial input and output cranks of equal radius. Brown omits the input crank from the small historical drawing; the gold input arm is added here to make its motion understandable. The outer retaining flange is behind the illustrated pin-travel plane.
The large view shows both cranks. The enlarged detail follows the output crank’s coordinates, so the contact wall or open passage is easy to inspect. Autoplay repeats a complete input revolution. Ring switching under power is not part of this animation.
Compare pin size, opening and motion
Crank radius sets the physical size. Pin diameter is entered as a fraction of that radius, and slot width as a multiple of pin diameter. These controls change the geometry used by both the animation and calculator.
The engaged example calculates ideal torque from a force normal to the slot wall and ideal power from rotational speed. The disengaged example checks whether the curved path of a finite-diameter pin clears the tangential opening. It does not assign a fractional torque to a partly engaged coupling.
Geometry used in the calculator
Let R be crank radius, d pin diameter, w slot width and a=1.5d the selected ring outer radius. In the engaged orientation the side clearance is c=(w−d)/2. The constant take-up angle is φ=asin(c/R). After take-up, the pin contacts the slot wall at x=c in the output crank’s frame.
For a force F normal to that wall, the moment arm is Rcosφ. Ideal torque is T=FRcosφ/1000 in N·m for R in mm; power is P=T(2πn/60)/1000 in kW.
For the open orientation, the pin center follows x=Rsinθ, y=R(1−cosθ) relative to the stationary ring center. A conservative clearance bound considers |x|≤a+d/2. The maximum near-pass sag within that interval is s=R−√(R²−(a+d/2)²). An opening w≥d+2s clears the whole pin through this region; extra allowance per side is (w−d−2s)/2.
This is a sufficient passage bound, not an optimized minimum. The selected input ranges keep the crank much larger than the ring and preserve clearance. The input period is 60/n seconds; at zero speed the model stops.
Example dimensions
With R=100 mm and d/R=0.12, the wrist pin is 12 mm in diameter. A slot ratio of 1.8 gives w=21.6 mm. The chosen ring radius is 18 mm.
The engaged side clearance is 4.8 mm, giving a take-up angle of about 2.75°. For a 500 N wall-normal force, ideal torque is about 49.94 N·m. At 30 rpm that corresponds to about 0.157 kW.
For the tangential passage, the conservative required opening is about 17.85 mm. The selected 21.6 mm slot therefore has about 1.88 mm extra allowance per side. These figures describe the chosen geometry, not a material or load rating.
Model boundaries
The ring and cranks are treated as rigid, and the pin is circular. The engaged animation begins with clearance already taken up; it does not simulate the initial impact. The open example holds the output at its rest position and shows the pin passing through.
Retaining hardware, axial clearances, lubrication, bending, contact stress, wear and switching forces require details beyond this planar model. No arbitrary shock multiplier or allowable clearance is presented as a design standard.
Slotted-ring coupling questions
Are forms 1 and 2 different couplings?
They are two settings of the same principle. The ring turns a quarter-turn between radial engagement and tangential passage.
Why does the open slot need more than one pin diameter?
The wrist follows a curved path. The extra opening allows for its sag while it overlaps the ring.
Why is the gold arm absent from Brown’s small figure?
Brown describes the input crank but omits it from the drawing. The illustration shows that arm in a separate axial plane to explain the motion.
Does the calculator predict a safe torque rating?
No. The engaged torque follows the entered wall force and geometry; no material-strength or contact-stress rating is calculated.
Primary reference
Henry T. Brown, 507 Mechanical Movements, movements 176 and 177, printed page 46. The paired drawings show the slotted ring in engaged and pass-through orientations. The dimensioned model adds a visible input crank and explicit geometric assumptions.
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