A globoid cam, or globoidal roller-gear cam, has a concave hourglass body whose working flanks engage rollers on an output turret. Its input and output axes are perpendicular. The cam profile can produce continuous rotation, oscillation or an index followed by a dwell. This example shows a continuously rotating cam advancing the turret one station at a time.
Globoid Cam Interactive Calculator
Choose the station count, the cam angle used for each index, a turret reference radius and the cam speed. The turret follows a cycloidal index and then holds still during the dwell. The gold surfaces illustrate local roller-contact flanks; the calculator describes the prescribed motion, not a production cam design.
Equation Used
N is the number of stations, β is the index portion of one cam revolution in radians, ωc is cam speed in rad/s, and R is the radius of the point whose tangential acceleration is calculated. One cam revolution gives one index. During the index, output travel is Δ[u−sin(2πu)/(2π)], with u from 0 to 1. The remaining cam angle is dwell. The peak-acceleration coefficient for this cycloidal law is 2π. The drawing keeps a normalized size; R changes the acceleration result. At zero cam speed, index time is undefined and speeds and acceleration are zero. These results do not determine follower contact force, total acceleration, preload, repeatability or bearing life.
The cam, rollers and turret
The cam’s waist accommodates the circular path of the turret rollers. Each roller turns on a radial stud carried by the turret. As the cam rotates, its working flanks move the engaged rollers and therefore the entire turret. Through the dwell portion, the input continues rotating while the output angle stays constant.
The animation shows the cam axis horizontally and the output axis through the turret face. All rollers keep the same spacing on the rigid turret. Gold strips show the local contact-flank geometry generated from the chosen motion; the blue hourglass shape is the cam core. Housing and bearings are omitted so both axes and the engaged rollers can be seen.
Roller-gear manufacturers use carefully formed working surfaces and controlled preload to reduce backlash. Preload, positioning accuracy and capacity depend on the actual design and adjustment. They cannot be inferred from a universal negative-gap value.
Cycloidal index and dwell
Let Δ=2π/N be one station step, Ti the index time and u=t/Ti during the index. The relative output angle is s=Δ[u−sin(2πu)/(2π)]. Its angular speed is ds/dt=(Δ/Ti)[1−cos(2πu)], and its angular acceleration is d²s/dt²=(2πΔ/Ti²)sin(2πu).
Speed and acceleration are zero at both ends of the index. The output then dwells until the next cam revolution begins. Peak output speed is 2Δ/Ti, and peak tangential acceleration at radius R is 2πRΔ/Ti². Radial acceleration Rωout² is a separate component and is not included in the tangential result.
The cam turns through β radians during the index, so Ti=β/ωc. Halving index time doubles peak speed and quadruples peak tangential acceleration for the same station step. A different motion law has different coefficients and must be calculated separately.
Example: eight stations at 60 cam rpm
With eight stations, each output step is 45 degrees or π/4 radians. At 60 cam rpm, one cycle takes one second. A 180-degree index portion takes 0.5 seconds and leaves 0.5 seconds of dwell.
Peak output speed is 2(π/4)/0.5=π rad/s, or 30 rpm. At a 100 mm reference radius, peak tangential acceleration is 2π×0.1×(π/4)/0.5²=1.974 m/s². The average output speed over the complete cycle is 60/8=7.5 rpm, which is lower than the peak during the index.
At 120 cam rpm with the same geometry and index angle, the index takes 0.25 seconds, peak output speed is 60 rpm and peak tangential acceleration is 7.896 m/s². This speed-squared increase does not by itself establish a bearing load or service life.
Choosing a fixed motion cycle
A mechanical indexer suits a repeated sequence in which a workpiece moves to a station and remains there for an operation. Assembly, packaging, transfer and tool-handling equipment are common application categories. The cam profile fixes the relationship between input rotation and output movement.
If a machine must change station spacing or dwell patterns frequently, a programmable drive may be more appropriate. For a cam indexer, changes to the motion pattern require an appropriate cam and follower arrangement; adjusting a speed control changes the time scale, not the station geometry.
From motion law to a working cam
A motion law specifies the desired output movement. Designing the physical cam also requires a roller arrangement, centre distance, flank envelopes, clearance, undercut and interference checks, bearing design, materials and lubrication.
The illustration uses radial cylindrical rollers and local envelope strips: at a calculated contact point, relative motion is tangent to the roller surface. It does not provide the complete trimmed flank surfaces or certify clearance between all solid parts. It is an explanation of the geometry and timing, not a machining model.
Neither a small measured gap nor an entered repeatability number predicts a complete indexer’s accuracy. Contact deformation, shaft and bearing stiffness, temperature, manufacturing error and the applied load also matter. Use the selected manufacturer’s specifications for operating limits and adjustment.
Frequently asked questions
Why does the turret stop while the cam keeps rotating?
The dwell portion of the cam profile holds the output angle constant. The input continues through that portion before the next index begins.
Is this a worm gear?
The parts have a related spatial appearance, but this example uses a shaped cam and radial rollers to produce a prescribed index and dwell. It is not a constant-ratio toothed worm pair.
What does the radius slider change?
It changes the tangential acceleration calculated for a point at that radius. The drawing is normalized for readability and does not resize the on-screen mechanism.
Does the acceleration result give follower force?
No. Follower force also depends on inertia, external torque, contact geometry, friction and the distribution of load between contacts.
Why does more dwell increase peak speed?
At a fixed cam rpm, more dwell leaves less time for the same output step. The turret must then reach a higher peak speed and acceleration during the index.
Does the model predict zero backlash?
No. It uses ideal prescribed motion. Actual backlash and stiffness depend on the manufactured flanks, roller bearings, preload and structural deflection.
Mechanism references
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