**6. Appendix: List of notation**


14 Will-be-set-by-IN-TECH

*Th\_x* Control

*Tr\_x* Collision response

7.3 7.25 7.2 7.15 7.1 7.05 7

Fig. 13. An augmentation of the third collision stage for torque feedback in the X axis, with

The real-time computation of the forces and torques in a virtual environment is a complicated task but a key point for the effectiveness of haptic systems. It is known that non-realistic or inappropriate haptic feedback has negative effects on the usability and leads to frustration when manipulating haptic systems. Therefore, it is very important to guarantee smooth and

This chapter outlines a haptic rendering method that computes a proper haptic response in complex environments. It ensures improved feedback by seeking a compromise between continuity and computational cost. The method avoids abrupt changes in the haptic force direction and magnitude, thereby improving the overall stability of the haptic system. In order to validate the proposed method, two different scenarios containing complex collision examples, such as multiple contacts and geometrical discontinuities, have been used. The

In terms of future research, the authors plan to analyze the performance of the method from a perceptual perspective carrying out studies of human factors to improve the responsiveness. The authors also hope that the research included in this chapter will provide a better understanding of the many phenomena that challenge the development of improved haptic rendering methods able to display adequate force and torque feedback while preserving

yielded results validate the applicability of the method in these types of interactions.

stability, and thereby improve performance of current haptic interfaces.

• **R***<sup>h</sup>* : User rotation of the haptic handle in angle-axis notation

Time (s)

0

and without applying the control algorithms

**5. Conclusions and future research**

realistic haptic feedback.

**6. Appendix: List of notation**

• *x, y, z* : Reference displacement axis

• **U***<sup>h</sup>* : User displacement of the haptic handle

0.2

0.4

0.6

Torque (Nm)

0.8

1

1.2

1.4


#### **7. References**


**Part 3** 

**Haptic Medical Modelling and Applications** 

