Gear Contact Ratio: Shared Tooth Engagement Is Not the Speed Ratio
Distinguish tooth-pair engagement overlap from the input-output speed ratio.
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Machine Guide Library — Page 25
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Worm Gear Starts: Count the Thread Starts Before Reading the Ratio
Count worm thread starts as well as wheel teeth before interpreting an ideal reduction ratio.
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Cam Pressure Angle: The Follower Motion Direction Changes the Force Projection
Use the defined cam pressure angle to distinguish normal contact force from useful follower force.
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Cam Dwell: Constant Shaft Rotation Does Not Mean Constant Follower Motion
Separate camshaft rotation from follower rise, dwell and return when describing a cycle.
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Cam Rise Angle and Follower Velocity: Keep the Displacement Function
Convert an explicit follower displacement function into velocity using the stated camshaft speed.
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Sliding and Rolling Cam Followers: Identify the Contact-Motion Assumption
Identify the contact motion assumed by a sliding or rolling follower model.
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Flywheel Working Energy: Use the Permitted Speed Change
Compare a cyclic work requirement with flywheel energy available between stated speeds.
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Friction-Clutch Slip: Relative Speed and Torque Define the Heat Model
Use relative slip speed when estimating a friction clutch’s illustrative heat input.
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Repeated Brake Stops: Heat per Cycle and Cooling Interval Are Different Inputs
Keep energy per stop and repetition timing together when reviewing brake thermal duty.
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Little’s Law: Match Inventory, Flow Rate and Time Boundaries
Relate average work inventory, flow rate and residence time using one defined system boundary and consistent units.
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Queue Waiting and Total Residence Time: Include Service Once
Use arrival, service-start and departure events to separate queue waiting from service and total residence time.
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Utilization: Keep Busy Fraction Separate from Nominal Speed
Calculate a resource’s occupied fraction over a defined window without confusing it with its speed while running.
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M/M/1 Stability: Demand Must Be Below the Model Service Rate
Check λ < μ and the stochastic assumptions before applying a finite steady-state M/M/1 queue result.
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M/M/1 Delay: Capacity Margin Changes the Predicted Waiting Time
Calculate M/M/1 average residence and queue waiting under explicit assumptions, and compare fictional capacity margins.
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Equal Average Arrivals: A Burst Can Produce a Different Queue
Compare explicit regular and burst arrival schedules with the same average rate and different FIFO waiting.
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Finite Buffers: Waiting Space Can Block an Upstream Station
Define the full-buffer response before modeling an upstream station’s ability to release completed work.
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Overlapping Model States: Summed Flag Durations Can Exceed Elapsed Time
Distinguish summed overlapping state-flag durations from the time during which at least one flag is active.
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Parallel Stations: Add Capacity Only Across the Defined Resource Paths
Calculate independent parallel service bounds and retain any shared-resource requirement limiting the combined path.
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Fork-Join Operations: Completion Waits for Required Branches
Use required branch completion events to define a fork-join boundary instead of summing independent parallel durations.
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Batch Release and Individual Transfer: The Same Work Can Wait Differently
Trace when individual jobs become available downstream under an explicit batch-release rule.
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Sequence-Dependent Setups: Retain the Previous and Next Product
Retain the ordered previous-to-next state in a setup-time matrix when comparing schedules.
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Re-Entrant Routes: One Station Can Be Visited More Than Once
Count every planned visit to a shared station when translating job rate into its modeled service demand.
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Decorated Containers on a Packaging Line: Agree the Finished-Pack Review
Review decorated containers through every planned machine contact and transfer, using incoming references and stage-specific finished-pack observations.
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Scrap Exit Boundaries: A Flow Balance Needs Every Outflow
Include accepted, rejected and other defined exits when reconciling modeled inventory change.
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