# KIN_TYP_11 – 5-axis kinematics with oblique tool head

## Kinematic structure

The kinematic structure consists of 3 translatory Cartesian axes and 2 rotary axes. As a special feature the machine has an oblique B axis.

Axis configuration in the NC channel
Axis identifier | X, Y, Z, A, B
Axis index | 0, 1, 2, 3, 4
Kinematic structure
| Tool axes | Workpiece axes
NC axes | X, Y, B | Z, A

Axis configuration of the 5-axis machine with oblique angle head
Angles and lengths at the oblique angle head

The design of the oblique B axis is the most striking feature of the kinematic structure. If the tool length is selected such that the TCP (tool centre point) lies exactly on the extension of the B axis (tool offset HDZ), no compensation motions are required in the translatory axes when the tool orientation via the B axis changes (compensation motions due to changes in A axis orientation are always present). If the selected tool length is not ideal (i.e. if the TCP is not exactly on the extension of the B axis), there are minor additional compensation motions on the linear axes depending on the deviation from the ideal length.

Due to the particular design of the B axis, there can be no singular points in the backward transformation of the orientation axes. On the other hand, not all tool orientations can be selected (see below).

The zero positions of machine axes XM, YM, ZM are selected such that the fictitious extensions of AM and BM intersect. The zero position of BM is selected such that the tool is in a vertical position and, consequently, parallel to Z0 if BM=0 (The figure “Axis configuration of the 5-axis machine with oblique angle head” shows the zero position of BM). Expediently, the zero position of AM should be selected such that the Y0, Z0 workpiece axes run parallel to the directions of the machine axes.

HDZ represents the ideal tool length as geometry parameter of the machine kinematics; HD1 represents the first tool head parameter; L is the actual tool length (milling cutter length).

Please note that l is a signed value and may also be negative.

## Offset data of kinematics

HD offset | param[i] | Description | Unit
HD1 | 0 | Z axis offset tool holding device to tool head reference point | 10 E-4 mm
HD2 | 1 | Ideal tool length | 10 E-4 mm
HD3 | 2 | Angle between B axis and Z axis (oblique angle) | 10 E-4°