A pendulum saw carries a circular blade on an arm that swings about a fixed pivot. Explore the arbor’s arc from a parked angle to the vertical position, and calculate blade-edge speed from diameter and rpm.
Pendulum Saw Geometry Explorer
Choose blade diameter, arbor speed, pivot-to-arbor length and parked angle. The worksheet reports ideal blade-edge speed and the arbor travel to the vertical working position.
Equation Used
- The arm is rigid and rotates about one fixed pivot.
- The blade arbor is at the declared distance A from the pivot.
- Parked angle is measured from vertical; the working position is directly below the pivot.
- Blade diameter and arm length remain constant through the animation.
- Cutting load, torque, tooth geometry, material, feed, structure, guards and safe operation are excluded.
The arm length and parked angle set the arbor travel. Blade diameter and rpm set the numerical edge speed. The animation is slowed and does not reproduce the entered arbor rpm or simulate cutting a workpiece.
A circular blade carried by a pivoted arm
WIPO patent publication WO2012084490A1 describes the defining arrangement directly: a circular saw blade mounted on a pendulum arm that swings around a pivot point. The explorer models that simplest single-pivot topology.
The animation keeps the pivot-to-arbor length and blade diameter invariant while the arm moves from the selected parked angle to the vertical working position and back. Blade rotation is deliberately slowed so the geometry remains visible.
Geometry for understanding the motion
The worksheet helps compare how arm length and parked angle change arbor travel. It is an explanatory geometry model, not a machine-selection or operating guide.
Real machines may add translating pivots, compound arms, guarded enclosures, powered feeds and control systems. Those details are not inferred here.
Rigid-arm travel and circular-blade speed
OpenStax gives arc length s=r theta and tangential speed v=r omega. Applying those identities gives arbor arc travel A alpha and blade-edge speed pi D N/60 when D is in metres and N is in revolutions per minute.
From the parked position to vertical, horizontal sweep is A sin(alpha) and vertical drop is A[1-cos(alpha)].
A declared geometry example
With a 500 mm blade at 1,750 rpm, ideal unloaded tip speed is about 45.81 m/s. A 900 mm arm parked 45 degrees from vertical travels an arc of about 706.9 mm; its arbor moves 636.4 mm horizontally and drops 263.6 mm.
Kinematics are not cutting performance
Blade-edge speed alone does not determine capacity, feed rate, force, power demand or cut quality. Those require material properties, tooth geometry, kerf, engagement, drive losses and a specific machine structure.
Use these results to compare geometric travel and blade-edge speed. Cutting capacity, motor demand and machine settings require data for the blade, material and complete saw.
Pendulum-saw calculation questions
Is tip speed the same as feed speed?
No. Tip speed describes the blade edge; feed speed describes motion through the work.
Why is the working position vertical?
It is a declared reference position directly below the pivot, chosen to make the single-arm geometry unambiguous.
Does the model predict cutting force or motor size?
No.
Can it be used as safety guidance?
No. It omits guards, controls, structure, braking and operating procedures.
Pendulum-saw references
- WIPO patent publication WO2012084490A1: circular blade on a pendulum arm swinging about a pivot.
- OpenStax University Physics, Rotational Variables: arc length and tangential-speed relations.
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