These cam sectors are paired portions of logarithmic-spiral wheels. They rotate about two fixed centers, with changing radii meeting at a common contact point. Their changing radius ratio produces a changing angular-speed ratio.
Linear actuator checks for Cam Sectors Mechanism
An actuator-driven version of cam sectors mechanism should be reviewed for stroke, linkage angle, and peak force. The mechanism may feel light through most of the travel and still bind or spike in force at one position.
For these paired sectors, check how the changing contact radii affect the required motion and force. A linear actuator attached through an additional linkage needs its own force-and-travel calculation; the sector speed ratio alone does not size it.
If the application needs synchronized motion, feedback should be treated as a requirement rather than an accessory. Two open-loop actuators wired together can drift apart when friction, load, or mounting geometry differs between sides.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Cam Sector Interactive Calculator
Set the center distance, spiral steepness and total input swing. Playback reverses through that range. The live results give both contact radii, their ratio and output angle.
Equation Used
- Paired equal-radius-at-center logarithmic spirals, rigid fixed centers.
- Rolling without slip and maintained contact are assumed; no traction, preload or tooth design is calculated.
- The sectors are limited-angle pieces, not full-turn cams.
- Steepness and swing ranges keep positive contact radii and contact within the illustrated sectors.
- No follower displacement, dwell timing, force or load rating is calculated.
Hiscox figure 1083 illustrates paired logarithmic-spiral sectors. Follow their common contact point and compare the changing radii, opposite rotations and instantaneous speed ratio.
Two contacting spiral sectors
Hiscox figure 1083 identifies cam sectors as sectors of logarithmic-spiral wheels. In the paired-wheel form, each pair of coincident radii adds to the distance between the fixed centers. As one sector turns, the contact point shifts along the line between those centers, changing the radius ratio.
The animation constructs both curves from the same logarithmic law. They share a tangent at contact throughout the selected swing. A no-slip rolling condition determines the opposite rotation of the second sector. The open webs and fixed shafts make the two distinct rotating pieces visible.
Exploring variable angular transmission
This historical arrangement illustrates how non-circular contacting profiles can produce a changing angular ratio over a limited range. It is distinct from a single cam segment driving a follower through rise, dwell and return.
The model is useful for comparing radius and angle relationships. It does not establish the preload, friction, teeth or structural dimensions needed to transmit a specified load.
Paired logarithmic-spiral geometry
Let D be the fixed center distance and k the logarithmic-spiral steepness. Both radii equal D/2 at the center position. For input angle u, rA = (D/2) exp(−k u), while rB = D − rA. The output angle is v = −ln[rB/(D/2)]/k. Angles in these equations are radians.
Differentiating gives dv/du = −rA/rB. The minus sign indicates opposite rotations; the calculator reports the magnitude rA/rB. This same relationship equates the tangential contact speeds when rolling occurs without slip.
A 200 mm center distance
With k = 0.20 and zero input angle, both contact radii are 100 mm and the speed-ratio magnitude is 1. At u = +20°, the first radius is approximately 93.26 mm, the second 106.74 mm and the ratio approximately 0.874. The output angle is approximately −18.69°.
Doubling center distance doubles both radii but leaves the angular relationship unchanged. Increasing steepness changes the ratio more strongly over the same input swing.
Limits of the illustration
The rolling relationship is a kinematic assumption. Smooth contacting sectors need an appropriate means of maintaining contact and transmitting tangential force. This calculator does not determine that traction, contact stress or load capacity.
The historical description also distinguishes pressure-cam versions in which the sum of radii varies. This demonstration uses only the fixed-center paired-wheel case, where the sum stays constant.
Questions about cam sectors
Why does the second sector turn by a different angle?
The contacting radii change during motion. Their ratio sets the local angular-speed ratio.
Why does changing center distance not change the visible overall width?
The view fits the mechanism to the available space. The live radius values and center-distance label update in millimeters.
Do these sectors produce a dwell interval?
This paired-sector mechanism has no follower dwell interval. Its two contacting spiral sectors transmit opposite rotation through a changing radius ratio over the selected angular range.
Does the speed ratio prove that a load can be transmitted?
No. It assumes maintained rolling contact. Traction and structural capacity require additional information.
Primary construction reference
Gardner D. Hiscox, Mechanical Movements, Powers and Devices, page 268, figure 1083: paired cam sectors or logarithmic-spiral wheel sectors, with coincident radii adding to the center distance.
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