Convert a total dwell angle and constant input speed into dwell time, cycle time and remaining non-dwell time. The accompanying rack-and-sector sketch illustrates reciprocation, but the two inputs do not determine its gear dimensions, stroke or engagement geometry.
Intermittent Reciprocating Motion Interactive Calculator
Convert total dwell angle and constant input speed to time. The rack-and-sector illustration shows a chosen motion sequence rather than calculated gear contact.
Equation Used
- Input speed is constant through one revolution.
- Entered dwell angle is the aggregate ideal geometric dwell across that revolution.
- Dwell boundaries are exact and the illustrated rack remains stationary during the entered dwell allocation.
- No module, pressure angle, tooth count/profile, pitch radii, centre distances, stroke, sector handoff geometry, backlash, loads, deflection, vibration, contact stress, wear, tolerances or safety model.
The angle is the total dwell allocation within one 360-degree input revolution. The remaining time is merely non-dwell time; the displayed rack stroke and sector phasing are explanatory because no module, tooth count or length input is provided.
Alternating sector gears and a double-sided rack
At constant N rpm, one input revolution takes 60/N seconds. A total dwell allocation theta_d occupies theta_d/360 of that cycle.
The sketch shows an input gear, two sector gears and a double-sided rack. The rack’s forward and return motion is prescribed independently of tooth contact, so the separated drawn parts do not establish a mechanically connected drive.
Convert a known dwell angle to time
The result can translate a known ideal dwell allocation and constant speed into aggregate time. It cannot determine required dwell, cam geometry, stroke, follower motion, or machine throughput.
Aggregate dwell only
Dwell time=(theta_d/360)(60/N). Remaining non-dwell time is cycle time minus dwell time and may include rise, return and any other motion intervals.
If a mechanism has two dwells, enter their total only when aggregate dwell time is the intended quantity; this calculator does not report each dwell separately.
Worked example
At 60 rpm, one revolution takes 1.000 s. A total dwell allocation of 90 degrees is 25% of the cycle, giving 0.250 s aggregate dwell and 0.750 s remaining non-dwell time.
What a physical rack drive requires
A physical rack drive needs compatible tooth pitch, center spacing, stroke and engagement timing between its sectors and rack. Loads, inertia, backlash and stiffness determine whether the motion can run accurately. The time conversion here cannot supply those dimensions or predict forces and service life.
Questions
Is remaining time the actual move time?
Only as an aggregate non-dwell allocation; the sector engagement law is not calculated.
Does the calculator determine stroke?
No. No module, tooth count, pitch diameter or length input is provided.
Is calculated dwell fully usable process time?
Not necessarily. Settling, compliance, backlash, controls and process margins reduce usable time.
Related mechanism video
Gear rack drive for linear reciprocating motion 2 by Nguyen Duc Thang illustrates a rack drive. This page’s timing calculator uses only entered dwell angle and speed; it does not calculate the video mechanism’s tooth geometry or stroke.
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