Hiscox’s horizontal boom tower carries a travelling trolley and an automatic shovel bucket. The trolley changes the bucket’s position along the boom. The calculator below is a separate rigid-vector coordinate exercise using entered pitch and slew angles; it does not model the historical trolley, bucket or hoisting ropes.
Rigid-Vector Coordinate Calculator
Project entered boom length through pitch and slew angles to forward, lateral and vertical coordinates, with an entered forward mast offset.
Equation Used
- One rigid straight vector of entered length from a fixed pivot.
- Pitch is measured from horizontal and slew about the vertical axis.
- Entered mast offset shifts only the forward coordinate.
- No joint limits, collisions, deflection, loads, hydraulics, stability, machine envelope or safety system.
The vertical result is rise relative to the boom pivot, not absolute tip height. The percentage is interpolation across the calculator's fixed 4–7 m input range, not physical actuator extension or recommended operating range.
Rigid-vector projection
The entered length is projected horizontally by cos(pitch), then resolved into forward and lateral components by the slew angle. Vertical rise is L sin(pitch).
The drawing shows a static entered vector. The play control does not move its endpoint because this exercise has no time-dependent motion model. It does not depict the historical trolley-and-bucket assembly.
Use as a coordinate check
The calculator can check a simplified mast-frame coordinate convention. It cannot determine reachability or suitability for any machine, task or site.
Coordinate transform
Horizontal projection is L cos p. Forward coordinate is L cos p cos s plus entered offset, lateral coordinate is L cos p sin s, and vertical rise is L sin p.
After removing the forward offset, the three components preserve vector length L.
Worked example
At L=7 m, pitch 0°, slew 0° and zero offset, the forward coordinate is 7 m and lateral and vertical coordinates are zero. At 90° pitch, horizontal coordinates collapse to the offset and vertical rise is 7 m.
Scope and limitations
A real machine envelope requires verified pivot and link geometry, telescope stages, feed and tool offsets, joint and hose limits, collision volumes, mast and carrier pose, load-dependent deflection, hydraulic limits, stability, ground conditions, controls and manufacturer-rated configurations.
Questions
Is vertical rise absolute tip height?
No. Add the actual pivot elevation and all relevant tool offsets.
Does 100% mean safe full extension?
No. It only means the length input equals the slider maximum of 7 m.
Is this a working envelope?
No. A working envelope must enforce all physical and safety constraints.
Historical source and calculation basis
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry 1214, identifies a horizontal boom tower with a traversing trolley and automatic shovel bucket.
The separate calculator uses elementary rigid-vector projections. It contains no trolley position, hoist-rope length, bucket linkage or load calculation, and does not establish the capabilities of a particular machine.
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