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Figure 2 | Journal of Mathematics in Industry

Figure 2

From: A computational method for key-performance-indicator-based parameter identification of industrial manipulators

Figure 2

A laser tracker measurement system for parameter identification of industrial manipulators. On the left, a laser tracker with a single reflector is presented. Here, the world frame is located in the foot of the manipulator. On the right, the figure shows the homogeneous transformations describing the manipulator and the laser tracker as well as the transition from the laser tracker coordinate system to the world coordinate system \({^{\mathrm{LT}}_{0}}\mathrm {T}\). Transition from joint \((i-1)\) to i is mathematically described by the homogeneous transformation \({^{i-1}_{i}}\mathrm {T}\). The reflector is mounted on the tool center point by the translation \({^{k}}\boldsymbol {c}_{j}\). Incident angle β between the reflector’s orientation vector 0 z in z-direction and the normalized laser beam 0 g from the reflector to the laser tracker is computed by \(({^{0}}\boldsymbol {z}^{T} \cdot{^{0}}\boldsymbol {g}) \cdot\|{^{0}}\boldsymbol {g}\|\).

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