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Robotics is an interdisciplinary field and there exist several well-known approaches to represent the dynamics model of a robot arm. The robot arm is an open kinematic chain of links connected through rotational and translational joints. In the general case, it is very difficult to obtain explicit expressions for the forces and the torques in the equations where the driving torques of the actuators produce desired motion of the gripper. The robot arm control depends significantly on the accuracy of the dynamic model. In the existing literature, the complexity of the dynamic model is reduced by linearization techniques or techniques like machine learning for the identification of unmodelled dynamics. This paper proposes a novel approach for deriving the equations of motion and the actuator torques of a robot arm with an arbitrary number of joints. The proposed approach for obtaining the dynamic model in closed form employs graph theory and the orthogonality principle, a powerful concept that serves as a generalization for the law of conservation of energy. The application of this approach is demonstrated using a 3D-printed planar robot arm with three degrees of freedom. Computer experiments for this robot are executed to validate the dynamic characteristics of the mathematical model of motion obtained by the application of the proposed approach. The results from the experiments are visualized and discussed in detail.

The orthopedic manipulation “bone drilling” is the most executed one in the orthopedic surgery concerning the operative treatment of bone fractures. The drilling process is characterized by a number of input and output parameters. The most important input parameters are the feed rate [mm/s] and the drill speed [rpm]. They play significant role for the final result (the output parameters): thermal and mechanical damages of the bone tissue as well as hole quality. During the manual drilling these parameters are controlled by the surgeon on the base of his practical skills. But the optimal results of the manipulations can be assured only when the input parameters are under control during an automatic execution of the drilling process. This work presents the functional characteristics of the handheld robotized system ODRO (Orthopedic Drilling Robot) for automatic bone drilling. Some experimental results are also shown. A comparison is made between the similar systems which are known in the literature, some of which are available on the market. The application areas of ODRO in the orthopedic surgery practice are underlined.

The orthopedic manipulation “bone drilling” is the most commonly used in the surgical treatment of bone fractures. The bone drilling process is characterized with a set of input and output parameters. The first ones define the conditions of the process execution and the second ones determine the outcome. The input parameters as feed rate [mm/s] and drill speed [rpm] have the most importance for the outcome, namely thermal and mechanical damages of the bone tissue.Many scientific researches related to the input parameters influence to the bone drilling process are published. The purpose is to find such an input parameters combination which is able to guarantee optimal result concerning the outcome parameters of the bone drilling process.The difference between the experimental results of many studies appears and even becomes bigger for the sake of wide variety of test conditions used by researchers. However, the following common dependencies stand out:-to avoid thermal osteonecrosis the drilling process must be executed with possibly maximal feed rate value together with possibly minimal drill speed value. -to avoid traumatic osteonecrosis the drilling process must be executed with possibly minimal feed rate value and possibly maximal drill speed value.So that the requirements concerning the drill speed and the feed rate values are contradictory and in the same time such values must be maintained during the bone drilling process aiming to obtain the optimal results. In manual drilling these parameters are controlled by the surgeon on the base of his practical experience. But the control of these parameters and the achievement of their optimal values can be successfully realized only under its robotized execution.Feed rate control during an automatic bone drilling process using an orthopedic drilling robot ODRO has already been introduced in our previous publications. The drill speed control is the next step in the development of ODRO.During bone drilling a significant amount of already done mechanical work directly converts into thermal heat elevated at the tool – bone interface. Since the critical temperature for thermal osteonecrosis is the most rigorously defined to be 47°C, the purpose of drill speed control during bone drilling process is to maintain the temperature below this critical threshold.Currently drill bit rotation in our case is realized on the base of MAXON BLDC controller/driver. With this type of controller, the motor speed is controlled entirely by hardware. It not allows software implementation of an algorithm for controlling the speed of the motor. The created and developed algorithm as well as the obtained and presented experimental results have a purpose to demonstrate the abilities of the controller TMCM 1630 for drill speed control during bone drilling process in dependence on the data characterizing the temperature deviation.This work presents basic characteristics of ODRO as well as a new drill speed control algorithm. It is one more additional step for improving the functionality of ODRO together with feed rate control during drilling and various specialized working regimes.

The bone drilling process is characterised by various parameters, the most important of which are the feed rate (mm/s) and the drill speed (rpm). They highly reflect the final effects and results of the drilling process, such as mechanical and thermal damages of bone tissue and hole quality. During manual drilling, these parameters are controlled by the surgeon based on his practical skills. But automatic drilling can assure an optimal result of the manipulation where such parameters are under control. During bicortical automatic bone drilling such a process consists of several stages: searching the contact with the first cortex, cortex drilling and automatic stop; searching the contact with the second cortex, cortex drilling and automatic stop; drill bit extraction. This work presents a way to control the feed rate during different stages of the bone drilling process (an original feed rate control algorithm) using the orthopaedic drilling robot (ODRO). The feed rate control is based on a proposed algorithm created and realised by specific software. During bicortical bone drilling process the feed rate takes various values in any stage in the range 0.5–6 mm/s. These values depend on drill bit position and real time force sensor data. The novelty of this work is the synthesis of an original feed rate control algorithm to solve the main problems of bone drilling in orthopaedic surgery – minimisation the drilling time (the heat generation); eliminating of the drill bit slip at the first (near) cortex and the drill bit bending at the second (far) cortex; minimising the risk of micro cracks which causes Traumatic Osteonecrosis; improving hole quality of the drilled holes; eliminating of the drill bit slip and the drill bit bending at the second cortex; minimising the value of the second cortex drill bit penetration by bicortical bone drilling.

The advanced tendency in development of robots oriented to orthopedic manipulations is maximally simplification of their mechanics. So called Handheld Robotized Systems appear. Here handheld bone drilling robotized system ODRO (Orthopedic Drilling Robot) is considered. The purpose is to compare its functional characteristics with the similar systems known in the literature. Experimental results are presented for porcine femur drilling by new drill module. The stop drilling decision is taken automatically. The information about experiments concerning the different modes is shown on the display after the drilling end. Handheld robotized systems can perform the accuracy and precise work like the stationary multifunctional robots. They do not need special software, pre-operative planning procedures, calibration, registration and systems for intraoperative navigation. In the same time they are much cheaper, accessible for usage, convenient for work and maintenance which will facilitate their mass application in the orthopedic surgery practice.

Development of hand-held surgical robot for automatic bone drilling George Boiadjiev 1,2 , Kamen Delchev 2 ,Tony Boiadjiev 3 , Rumen Kastelov 4 , Kazimir Zagurski 5 1) Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria 2) Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria 3) Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria 4) Orthopaedic and Trauma Clinical Centre of Ministry of Domestic Affairs, Sofia, Bulgaria 5) Institute of system engineering and robotics, Bulgarian Academy of Sciences, Sofia, Bulgaria This paper represents the development of a prototype robotic system for automatic bone drilling in orthopedic surgery. Answering the surgical requirements for the robot dimensions and weight to be as small as possible a new design of the mechanical structure is proposed. The new structure design is based on idea of parallelism of the axis of the linear actuator and the axis of the rotary one. The control system is improved by using of a new micro-controller. A new type of linear drive and a new force sensor (load cell) are built in so that the quality characteristics of the “Orthopedic bone Drilling Robot” (ODRO) are not only the same as previous its versions [1, 2] but become better. An experimental setup is arranged and experiments are executed to test and verify the robot quality features and functional capabilities. References 1. G. Boiadjiev, T. Boiadjiev, V. Vitkov, K. Delchev, R. Kastelov, K. Zagurski, Robotizeed System for Automation of the Drilling in the Orthopedic Surgery. Control Algorithms and Experimental Results., Proceedings of the 9th IFAC International Symposium on Robot Control (SYROCO 2009), Gifu Japan, September 9-12, 2009, pp 633-637, (2009). 2. Boiadjiev, G., Kastelov, R., Boiadjiev, T., Kotev, V., Delchev, K., Zagurski, K., Vitkov, V., Design and performance study of an orthopaedic surgery robotized module for automatic bone drilling, International Journal of Medical Robotics and Computer Assisted Surgery, 9(4), pp. 455–463, (2013).

This work presents the development of a redundant planar robot created with a 3D printer. The mechanical structure and the main kinematic dependencies are discussed. The hardware and software implementation of the prototype are presented. An algorithm is presented to find solutions of the inverse kinematics problem in the presence of obstacles in the workspace of the robot. The algorithm gives results on possible solutions both in the Cartesian coordinates and joint angles. The proposed software and the obtained results are the basis for planning trajectories of the robot in complex environments with obstacles. The created prototype is used for education of students in robotics and mechatronics. The advantages of using 3D printing technology in modeling and design and its application in the education process are highlighted.

Bone drilling manipulation often occurs in the orthopaedic surgery. By statistics, nowadays, about one million people only in Europe need such an operation every year, where bone implants are inserted. Almost always, the drilling is performed handily, which cannot avoid the subjective factor influence. The question of subjective factor reduction has its answer - automatic bone drilling. The specific features and problems of orthopaedic drilling manipulation are considered in this work. The automatic drilling is presented according the possibilities of robotized system Orthopaedic Drilling Robot (ODRO) for assuring the manipulation accuracy, precision, reliability and safety.

The development of manipulative systems oriented to concrete orthopaedic manipulations is an advanced tendency aiming maximally simplification of robot mechanical system. As a result so called Handheld Robotized Systems appear. They have the accuracy like the universal multifunctional robots and in the same time they are much cheaper, user-friendly and easy for maintenance.

The need of the most precise manipulations in the orthopedic surgery concerns spine. The drilling takes place very often there. If spine cortices are broken by mistake then fatal problems appear as paralysis, block of breathing and death. Therefore in operation as pedicle drilling the far cortex perforation must be avoided. This paper shows that it can be done by bone drilling hand-hold robot ODRO. It is able to detect the bone far cortex and stops just before contact registration. Experimental results are presented. Also the results based on new algorithms and software are presented and discussed.

Background: Currently, applications of robotized systems in orthopedic trauma surgery steadily increase due to their functional abilities facilitating surgeon skills. The aim of this study is to present the functional advantages of a recently developed robot for bone drilling. Methods: Ex-vivo experiments were performed on fresh porcine and bovine bones, as well as on fresh and embalmed human bones such as femora, vertebrae and rips, by the use of the robot for bone drilling to identify diverse control parameters and analyse thrust force and drill bit temperature during drilling. Results: Experimental data during drilling is shown, control algorithms are described and bone drilling modes are characterized. Maximal values of thrust force and temperature are detected. Controlling thrust force seems to be the proper way to reduce force resistance and hence temperature during drilling. In automatic drilling mode, preliminary defined channel depth is drilled with accuracy of 0.1 mm, and far cortex end recognition is proved to work reliably for automatic stop with minimal controlled soft tissue penetration. Cortex and bone marrow thickness are measured and analysed in real time. Conclusion: The bone drilling robot is programmed to follow with high accuracy parameters defined by the surgeon. Enhancing surgeon’s freedom and responsibility to make decisions, it can perform precise manipulations, decreasing the influence of subjective factors and increasing patient’s safety.