In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

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Milling forces play an important role in the milling process and are generally calculated by the mechanistic or numerical methods which are considered time-consuming and impractical for various cutting conditions and workpiece-tool pair. Therefore, this paper proposes an analytical method for modelling the milling forces in helical end milling process based on a predictive machining theory, which regards the workpiece material properties, tool geometry, cutting conditions and types of milling as the input data. In this method, each cutting edge is discretized into a series of infinitesimal elements along the cutter axis and the cutting action of each element is equivalent to the classical oblique cutting process. The three dimensional cutting force components applied on each element are predicted analytically using this predictive oblique cutting model with the effect of cutting edge radius. Finally, the proposed analytical model of milling forces is verified by the published results and the simulation values using the software AdvantEdge FEM.

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