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Usually, a special toolholder is used to hold the cutting tool firmly during operation.
A disposable glass micropipette is fitted to a toolholder mounted on the output of the manipulator.
The toolholder or machine taper itself is held by the drawbar and applies force to the spindle, especially when spinning at high speeds.
There's even a toolholder for small taps, and bitholders (magnetic or not) for hex screwdriver bits.
These began in the 1840s with the adaptation of the engine lathe with a turret-head toolholder to create the turret lathe.
Shapers, slotters, and planers often employ a kind of toolholder called a clapper box that swings freely on the return stroke of the ram or bed.
The toolpost is the part of a metalworking lathe which either holds the tool bit directly or holds a toolholder which contains the tool bit.
The synthetic diamonds are "grown" in small sizes at high temperatures and pressures and then brazed onto the part of the tool, known as the insert, that goes into the toolholder on the cutting machine.
The purpose is to allow a quick and easy change between different tools (either automatically or by hand) while ensuring the tool or toolholder will be tightly and rigidly connected to the spindle, and accurately coaxial with it.
It evolved from earlier lathes with the addition of the turret, which is an indexable toolholder that allows multiple cutting operations to be performed, each with a different cutting tool, in easy, rapid succession, with no need for the operator to perform setup tasks in between, such as installing or uninstalling tools, nor to control the toolpath.