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. 2023 Jan 12;13:598. doi: 10.1038/s41598-023-27467-w

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Position and force–time waveform of the master and slave units on the haptic drill. (A) The distance the drill advanced after penetration was defined as the distance that the slave advanced before the device detected the penetration and started retracting the drill. (B) This is a magnified view of the waveform, especially during penetration. The horizontal axis shows time, and the vertical axis shows reaction force. The waveforms are magnified to emphasize the changes in the waveforms during penetration. ① Shows the time required for penetration detection. ② Shows the distance advanced by the drill after penetration. (C,D) The distance travelled after penetration was defined as the distance travelled from "the position where the drill started to move forwards rapidly" to "the peak of the drill (slave) position", i.e., the distance travelled until the surgeon detected the penetration and started to retract the drill body. ① shows the time required for penetration detection. ② shows the distance advanced by the drill after penetration.