Determination of 5-axis tool orientation using analogy between parametric surface and form shaping function


Computer-aided manufacturing (CAM) systems have been developed for different industrial operations. These systems work hand in hand with numerically controlled machining tools to improve the quality and precision of machining operations. In particular, simultaneous 5-axis computer numerically controlled machine tools are widely used in different aspects of manufacturing. However, tool paths generation has remained a great challenge leading to numerous research work.

For the tool paths generated using the CAM software, the accuracy and quality of the resulting surface depends on the tool orientation and rotational axes. Therefore, proper choice of tool orientation and tool path optimization will ensure creation of smooth paths for efficient machining by eliminating possible singularities and collisions between the tool and the workpiece. Among the proposed approaches for preventing collisions in simultaneous 5-axis control, the configuration space has exhibited great potentials. It shows the relationship between the tool orientation and collision regions. Unfortunately, these methods employ the use of various constraints conditions for determining tool orientation. Up to date, constraining the 5-axis tool and especially those involving arbitrary axes have not been fully explored.

To this note, Dr. Keigo Takasugi, Yasutomo Sugisawa and Professor Naoki Asakawa from Kanazawa University presented a new constraint condition for determining unique tool orientation. Specifically, the approach was based on the analogy between the form-shaping function and the parametric surface of a target machine tool. This work is currently published in the research journal, Precision Engineering.

In brief, the importance of penetrating the form-shaping function using a geometric based approach was assessed. Next, the travel amounts of 5-axis derived using the form shaping function were converted into geometrical problems on a parametric surface. This led to the generation of axis travel amount surface (ATAS) owing to the equivalence of the constraint on the travel distance in the arbitrary axis and the geometric intersection on the parametric surface. Eventually, the contribution of the generated axis travel amount surface in determining the tool orientation was evaluated.

An intersection line observed between the surface and plane provided a constraint for fixing specific axes on the machine tool thus enabled constraining of the tool orientation selection for determining the tool path by maintaining the arbitrary axes in a fixed position. Additionally, the method exhibited good compatibility with the tool configuration space. For instance, the parametric space comprised of two parameters of the parametric surface that was analogous to the configuration space. This meant that by also constraining the arbitrary axes, the collision avoidance of the 5-axis tool path could be as well considered geometrically.

As a concept proof, the authors demonstrated two scenarios without collision avoidance and one based on configuration space using simulations. The first two cases showed the tool path generation based on two constraints using the ATAS while the last case showed the feasibility of the approach to avoid collisions between the tool and the workpiece. The results were further validated by an s-N map that presented an algorithm for searching tool path satisfying several constraints for generating a collision avoidance tool path. Furthermore, the method proved effective for limiting the number of operational axes.

In summary, the method presented by Keigo Takasugi and colleagues in the study will be significantly used by CAM developers and operators to determine algorithms and tool paths based on visible representations. This will improve the efficiency and quality of machine operations.

Determination of 5-axis tool orientation using analogy between parametric surface and form shaping function - Advances in Engineering

About the author

Dr. Keigo Takasugi

2006- Yamazaki Mazak Corp.
2012- Dr. Eng., Kanazawa University
2013- Assistant Professor, Kanazawa Institute of Technology
2016- Assistant Professor, Kanazawa University
Webpage (JP only):


Takasugi, K., Sugisawa, Y., & Asakawa, N. (2019). Determination of 5-axis tool orientation using analogy between parametric surface and form shaping function. Precision Engineering, 58, 7-15.

Go To Precision Engineering

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