Brownell’s crank motion places its wrist pin on a tangent slide carried by a rotating faceplate. A volute spring biases the slide toward its forward position, and pins running in elongated slots retain it. Hiscox describes its use with a treadle to help keep the crank pin off center.
The animation exposes the sliding carrier, guide pins, spring, connecting rod and rocking treadle. The calculator compares a selected slide offset and exact linkage geometry. Spring response and dwell are outside this geometry calculation.
Brownell Crank Motion Interactive Calculator
Move the wrist pin along its tangent slide and compare effective crank radius, phase and treadle motion. The selected slide offset is held during each turn; spring response is not simulated.
Equation Used
- Held tangent-slide offset during each revolution.
- Treadle pivot F=(2r,−4r), driven arm 2.5r.
- Rigid rod, planar pins and complete-rotation geometry.
- Spring and frame are illustrative; no force, preload or starting guarantee.
Construction after Hiscox figure 1113, with selected illustrative proportions. The slide offset stays fixed during each turn; spring force and automatic off-center behavior are not calculated.
The interactive animation above shows Brownell’s tangent-slide carrier, faceplate, connecting rod and rocking treadle.
A crank pin that can shift on the faceplate
The slide travels across the radial line on a tangent, rather than simply changing the length of a rigid crank. Moving it changes both the distance and angular position of the wrist pin relative to the shaft. The two fixed faceplate pins remain inside the slide’s elongated slots.
The gold connecting rod joins the wrist to a rocking treadle. The displayed rod and treadle retain their lengths throughout the turn. Below the animation, a faceplate-fixed detail makes the carrier’s selected position easier to inspect.
The spring is drawn as a flat spiral with a tail to the carrier, following the historical volute-spring description. Its stiffness, preload and contact behavior are unknown. The offset stays at the user-selected value during each turn; this is a geometry study, not a prediction of load-dependent spring movement or self-starting performance.
What the inputs show
Radial distance scales the physical mechanism. Tangent-slide offset changes the wrist’s effective radius and phase. Connecting-rod ratio changes the treadle’s angular excursion while keeping the linkage closed. Shaft speed determines cycle time; playback is slowed for inspection.
The treadle pivot is placed two radial distances to the right and four below the shaft, and its driven arm is 2.5 radial distances long. These are selected model proportions; the historical engraving does not supply these dimensions. The input ranges permit complete rotation for this chosen arrangement.
Held-offset geometry
Let r be radial distance, u the selected tangent-slide offset and θ the faceplate angle. In faceplate coordinates the wrist is (u,r). In stationary coordinates it is C=(u cosθ−r sinθ,u sinθ+r cosθ).
Effective radius R=√(r²+u²); phase shift=−atan2(u,r)
The treadle pivot is F=(2r,−4r), arm length b=2.5r and rod length L=r×rod ratio. The moving treadle pin T is the continuous left-hand intersection of |T−C|=L and |T−F|=b.
With ground distance G=√20 r, define α(q)=acos[(G²+b²−q²)/(2Gb)]. The treadle angular excursion is α(L+R)−α(L−R). These are the two positions where the crank and connecting rod align. Cycle time is 60/N seconds at N rpm.
These equations describe a fixed selected slide position. They do not establish a dwell angle, impact speed, torque capacity or spring force.
Default geometry
At r=50 mm and u/r=0.25, the slide offset is 12.5 mm and the effective crank radius is about 51.54 mm. Its phase shift is −14.04° relative to the radial line. A rod ratio of four gives a 200 mm connecting rod. At 40 rpm one turn takes 1.5 seconds.
Changing the offset sign reverses the phase shift. Equal positive and negative offsets have the same effective radius and treadle excursion in this held-offset model.
Model boundaries
Hiscox figure 1113 is the construction reference. The spring shape, guide proportions, treadle dimensions and offset range are selected to illustrate the arrangement. No spring force or load-dependent movement is solved.
Holding the slide offset fixed makes its geometric effects clear: changing the offset changes the wrist radius and phase, while the connecting rod remains the same length. Spring stiffness and loads are needed to predict movement of the slide during operation.
At zero speed the mechanism stops, but the cycle slider remains available. This is a rigid planar geometry demonstration, not a manufactured assembly or a guarantee that a treadle will start from every position.
Brownell crank questions
Does the slide move automatically during playback?
No. The selected offset is held so its geometric effect can be compared. Predicting spring movement needs spring and load data that the historical source does not provide.
Why does offset change the crank radius?
The wrist lies at both a radial distance and a tangent offset from the shaft. Its true distance is their vector magnitude.
Is this an ordinary offset slider-crank?
No. The sliding carrier is on the rotating faceplate, and the output shown is a pivoted treadle.
Does this model calculate a dwell interval?
No. It calculates motion with a fixed slide offset. That assumption does not establish an interval during which the treadle stays stationary.
Construction reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 274, figure 1113: Brownell crank motion with tangent slide, retaining pins, volute spring and treadle.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
