Annals of the CIRP Vol. 56/1/2007 -405- doi:10.1016/j.cirp.2007.05.094

Development of a Medical CAD/CAM System for Orthopedic Surgery

M. Mitsuishi1 (2), N. Sugita1, K. Fujiwara2, N. Abe2, T. Ozaki2, M. Suzuki3,H. Moriya3, T. Inoue4, K. Kuramoto4, Y. Nakashima4 and K. Tanimoto5

1Department of Engineering Synthesis, School of Engineering, The University of Tokyo, Tokyo, Japan 2Graduate School of Medicine and Dental, Okayama University, Okayama, Japan

3Graduate School of Medicine, Chiba University, Chiba, Japan 4Nakashima Propeller, Co. Ltd., Okayama, Japan, 5CORETEC INC, Okayama, Japan

Abstract In successful knee arthroplasty, the femur and the tibia must be shaped to fit an artificial joint. The recent trend towards MIS (Minimally Invasive Surgery) to decrease the length of the required incision in the skin has increased surgical difficulty, since the open access area is small. The developed system consists of (1) a preplanning system providing a CAD function, (2) a multi-axis CAM system which avoids cutting the skin and the ligament, and keeps the cutting time within acceptable limits, and (3) a 7-axis machine tool that assures the safety of the patient and the surgeon, and enables MIS.

Keywords:CAD, CAM, Biomedical

1 INTRODUCTION Total knee arthroplasty (TKA) and unicondylar knee arthroplasty (UKA) are orthopedic surgeries performed to reduce pain caused by the destruction of a joint by osteoarthritis or rheumatoid arthritis, and to enhance the QOL (Quality of Life) of the patient. In the surgical operation, the damaged articular portion of the bone is excised to fit the shape of the setting plane of the artificial joint and the original joint is replaced by the artificial joint. It is reported that the number of the patients who are suffering from osteoarthritis is from 12 to 20 % of the total population. The number is expected to increase rapidly due to the aging trends in developed countries.In TKA/UKA, the setting position and orientation of the artificial joint affect the inferior limb position after the operation. Therefore, postoperative pain and reduction in the useful lifespan of the artificial joint will occur if the artificial joint is not properly fixed and high accuracy of the cut surface is required. However, the accuracy of the cut typically depends on the surgeon’s skill, since the bone is shaped by hand. Therefore, the authors have been developing a system to assist in TKA/UKA and to increase the accuracy of the bone cutting. The paper describes, in particular, a medical CAD/CAM system for minimally invasive surgery (MIS), targeting TKA/UKA. The differences between the medical CAD/CAM system for knee arthroplasty and conventional CAD/CAM systems for metal cutting are listed as follows: 1. In case of metal cutting using a multi-axis machine

tool, the positions of obstacles can be predicted from the shape of the mechanical part being machined and the structure of the machine tool. However, in case of knee arthroplasy, the position of the soft tissues, such as skin and ligament, can only be determined after cutting the skin. Therefore, it is impossible to determine the location of the obstacles before starting the surgical operation. Correspondingly, a near real-time function to do the required planning and a user interface for the surgeon must be provided.

2. The length of the skin cut in conventional knee arthroplasty is approximately 150 mm, whereas the system described in this paper targets an incision of only 80 mm in length. This short incision necessitates

a sophisticated obstacle avoidance function, since the insertion area for the cutting tool is quite small.

3. The relative positions of the femur and the tibia relative to the bone cutting machine tool must be known with high accuracy. Therefore, a registration process is necessary.

4. Multi-axis functionality is required to machine the complex geometries that are required. In addition, the safety of the patient and the surgeon must be ensured and adequate irrigation and sterilization capabilities must be provided in a machine tool for medical use.

2 RELATED WORKS Orthopedic surgery assisted by a robot is considered to be (1) a process planning problem to machine an object of indeterminate shape into the specified shape, and (2) a toolpath planning problem to cut a deep and wide area of the bone by inserting a cutting tool through a small skin incision. The process planning problem is considered to be similar to the reconstruction of scanned data on a CAD system in reverse engineering. Toolpath planning has been discussed as a toolpath planning problem for a multi-axis machine tool and an obstacle avoidance problem in robotics. For example, Krause, et al. reconstructed laser scanned data on a CAD system using a neural network [1].ElMaraghy, et al. discussed the use of laser scanning in reverse engineering [2]. Concerning constructing and sharing a database for a CAD system, Kimura, et al. have been utilizing an expert knowledge based approach for a CAD/CAM system [3]. Noël, et al. are proposing a CAD system which has the ability to share knowledge and know-how [4].Regarding toolpath planning in the CAM system, Galantucci, et al. are applying a neural network and a genetic algorithm to provide registration while cutting free-form shapes [5]. Takeuchi, et al. applied the configuration space method, which is used in the automatic path planning of a robot manipulator, to 5-axis machining to solve an interference problem [6]. Lauwers, et al. are proposing a toolpath generation algorithm to optimize the cutting tool orientation based on the facet model for a multi-axis machine tool [7]. Lartigue, et al. are proposing a

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Post processorand axis control

Bone cutting machine tool

Medical image(CT, MRI, X-ray, etc.)

Preoperative CAD 3D position sensor

Registration

CAM

IntraoperativeCAM

Postoperative evaluation system

Figure 1: Developed medical CAD/CAM system.

tool path format which is applicable to a high speed machine tool, using the native polynomical format [8].Pritschow, et al. presented the design of and test results for a fail-safe numerical control (NC) for robotic surgery, which has assisted in a wide range of surgical treatments [9]. ROBODOC is one example of the introduction of a CAD/CAM system into the medical area that has many clinical applications. Its target is, however, mainly hip surgery. Therefore, it cannot be used effectively in knee surgery, where the surgical field is surrounded by soft tissues. Furthermore, there is a possibility that uneven wear of the joint may result because the planning system has not adequately considered the lateral and medial ligament balance [10]. Recently, surgeon-assisting and bone-mountable type systems have been proposed. For instance, ACROBOT, which has been developed by Davies, et al., is of the former type and has a mechanical guide function [11]. Dombre, et al. developed the BRIGHT system [12]. Mechanical jigs for a bonesaw are installed at the tip of the system. Kwon, et al. developed the ARTHROBOT which is aimed at minimally invasive hip surgery [13]. Plaskos, et al. developed a bone-mountable type cutting guide for the bonesaw [14]. However, the system has a problem because the length of the skip cut is extremely large. The importance of medical CAD/CAM systems is increasing because high precision and minimal invasiveness are the key technologies needed to advance skeleton surgery. Under the situation desribed above, the features of the developed system are as follows: (1) The authors have developed a multi-axis bone cutting machine tool for knee surgery in which the cutting tool is surrounded by soft tissues. (2) The system performs minimally invasive surgery with a small incision. (3) A medical CAD/CAM system that provides safety, irrigation and sterilization was developed.

3 OVERVIEW OF THE DEVELOPED SYSTEM

3.1 Requirements of minimally invasive surgery for TKA/UKA

The required issues for the TKA/UKA are as follows: (1) extension of the useful lifespan of an artificial knee joint by setting it at the appropriate position and posture, (2) increase of the fixture force by cutting the bone accurately, and (3) minimal invasiveness aiming at the early recovery of a patient. Minimal invasiveness means a small incision. The opening area for the cutting tool is small and narrow. Therefore, the collision of the cutting edge with a soft tissue should be avoided not to damage the surrounding soft tissues, such as skins, ligaments, blood vessels and nerves. Consequently, a method to cut the bone for an artificial joint without damaging the surrounding tissue is required.

3.2 System configuration The authors have developed a system to assist in minimally invasive surgery as shown in Figure 1. The features of the developed system are that it recognizes the position of the soft tissue accurately during surgery and that the toolpath is generated using the information.

3.3 Preoperative system as a CAD system The shape of the bone is obtained by taking a CT image of each patient and reconstructing the 3D shape of the target bone from the sliced data. The position and the size of the artificial knee joint is determined based on the clinical knowledge incorporated in the preoperative planning system.

3.4 Registration and CAM system including toolpath generation for minimally invasive surgery

The position and the orientation of the bone are described with reference to the bone cutting machine tool coordinate system using the information from the registration process. A minimally invasive toolpath considering the actual size and location of the entry incision is generated in the CAM system, based on the configuration and the shape of femur and tibia. As shown in Figure 2, 5 planes at the distal part of the femur and 1 plane at the proximal part of the tibia are cut accurately by the bone cutting machine tool to fit the artificial joint shape.

3.5 User interface The surgical protocol used for the bone cutting machine tool in knee arthroplasty is shown in Figure 3. The protocol during the surgery is as follows: skin cut, preoperative planned data reading, registration, fixture of the target bones, skin cut area measurement, toolpath generation, and bone cutting. Each surgical process is guided by the user interface. In the developed user interface, the surgeon is asked to confirm the preplanned data with the actual position by displaying the patient information at any time, to increase the safety of the total system. Furthermore, a wizard format is adopted for the user interface, so as not to make a mistake during the actual surgical procedure. The shape of the bone is displayed on the screen, as well as the necessary numerical data needed to confirm it intuitively.

Tibia

Femur

Base plate

Polyethyleneplate

Femurcomponent 1

234 5

6

Figure 2: Shape of an artificial knee joint.

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4 PREOPERATIVE PLANNING SYSTEM AS A CAD SYSTEM

4.1 Overview of the system It has been difficult to determine the accurate 3D position of an artificial joint in conventional systems because the preoperative planning is executed using a 2D X-ray image. To overcome this problem, the authors have developed a preoperative planning system to determine the setting position of an artificial joint using the 3D bone shape as shown in Figure 4. The required functions for the preoperative planning system to achieve the high precision and minimally invasive surgery are discussed in the subsequent subsections.

4.2 Reconstruction of bone shape 3D bone shape is reconstructed using CT sliced images to determine the setting position of the artificial knee joint precisely. The projection surface interpolation type APP (Average Pixel Projection) [15] method was adopted to reduce the processing time without interpolating 3 dimensionally. The bone shape for toolpath planning was generated using the binary information referenced to the CT value, after determining the position of the artificial

joint.Machine tool initialization

Incision

Setting markers for 3Dposition

Characteristic pointsacquisition

MeasurementMedical operation Setting

Workpiece (femur andtibia) registration

Fixation of a patient

Toolpath generation

Machining of Tibia

Machining of Femur

Implant insertion

Setting 3D positionequipment

Opening areameasurement

Machine toolpositioning

Registration ofthe machine tool

Checking ligamentbalance

Figure 3: Knee arthroplasty protocol.

4.3 Separation of bone information The toolpath should be planned separately, even though the artificial knee joint is located at the distal and proximal part of the femur and the tibia, respectively. Furthermore, it is required to generate a toolpath that only cuts the bone, so that the cutting tool does not damage the surrounding soft tissues. However, generally, the leg configuration obtained by the CT image differs from that during surgery because the relative position between the femur and tibia varies. Therefore, it is required to construct the 3D shapes of the femur and the tibia. Information for the femur and tibia was separated because both femur and tibia information was included in the CT images obtained around the knee joint. Then the 3D shape was reconstructed individually.

4.4 Extraction of feature points The load axis and the surgical epicondyle axis (SEA) are used as a standard line to determine the setting position of an artificial joint. Feature points to draw the standard lines are extracted from the 3D bone shape. As the femur and the tibia are located at arbitrary positions and orientations to the fixture jigs, preoperatively planned data should be transformed to the bone cutting machine tool coordinate system. Feature points are used as matching points during the coordinate system transformation. The positions of the feature points and the artificial joint are determined using the preoperative planning system with the functions mentioned above. The size of the artificial joint is selected based on the 3D bone shape. The cutting areas for the femur and tibia are described with reference to the local coordinate frame of the artificial joint A, which is fixed to each cut surface. The local coordinate frame of the artificial joint is presented with reference to the artificial joint coordinate frame B. The final position of the artificial knee joint, feature points and the shape of femur and tibia are presented with reference to the preoperative planning coordinate frame C, and transmitted to the CAM system.

5 REGISTRATION AND COORDINATE SYSTEM TRANSLATION

An infrared coordinate measurement system was adopted to measure the position and the posture of the bone. In the system, reflective markers are attached to the bone so that they are visible from the infrared measurement system and do not disturb the surgical operation. The bone coordinate frame D is located at the infrared marker.The length of the skin cut is small in minimally invasive surgery. This increases the difficulty in measuring the total shape of the bone because it is located behind the skin. Therefore, same points are measured, which are determined during preoperative planning. More concretely, 8 and 5 points are used for the femur and tibia, respectively, including the femur head, as shown in Figures 5 and 6. The position of the femur head is measured by reading the position of the infrared marker multiple times while moving the leg around the femur head. The bone shape and position of the artificial knee joint, which are described by the preoperative planning coordinate frame C, are transformed into those described by the bone coordinate frame D, to minimize the distance between the feature points used in the preoperative planning and the points specified during the surgical operation. Each bone shape, which is presented with reference to the preoperative planning system, is estimated by representing it in the bone coordinate frame D. The bone coordinate frame D is defined with reference to the static coordinate frame E. Now the total bone shape

Matching

Femur front

Femur implant

Tibia side

Tibia implant

Patient informationPatient IDPatient nameHospitalDateOthers

Implant Rod

Size

Height

MatchingImplant position

New Print Restart Save Up Dn Region Move Redraw Init Display Thresh 4 2 Front Side Cross Exit

Detail Front view Side view

Reconstructedbone surface

Implantposition/sizeplanning

Femur

Tibia

Femur

Tibia

Menu area

Figure 4: Preoperative CAD system.

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is defined at the arbitrary position and orientation for the femur and tibia. For the next step, the skin incision area is measured with reference to the static coordinate frame E. An infrared marker is attached at the tip of the bone cutting machine tool and the bone cutting machine tool coordinate frame Fis defined with respect to the marker. Bone information is transformed with reference to F by measuring the Infrared marker on the bone cutting machine tool from the static coordinate frame E. Finally, toolpath data determined with reference to the local coordinate frame of the artificial joint A is transformed into the data presented with reference to the bone cutting machine tool coordinate frame F. Then

the data to control the bone cutting machine tool is generated as shown in Equation (1)

TTTTTT FE

ED

DC

CB

BA

FA

, (1)

where presents the transformation from coordinate

systems m to n. is defined for 5 and 1 planes for femur and tibia, respectively. and are defined for the femur and tibia, respectively.

TnmTBA

TCB TDC

6 TOOLPATH GENERATION FOR MIS

6.1 Overview of the system In minimally invasive orthopaedic surgery, the cutting tool needs to approach the target through the small hole and resect the large area inside the joint. The opening area and the positions and attitudes of the femur and tibia are measured by an infrared positioning sensor, and the workspace for the operation is defined precisely. A toolpath generator is developed to avoid collisions with the surrounding soft tissues.

6.2 Measurement of incision area The opening area is measured with a 3-dimensional optical position sensor as depicted in Figure 7. The border of the area is measured as the points for the opening plane. Based on the stored data, a regression analysis is used, and equation (2) is computed.

2)( c) b, J(a, cbyaxz iii (2)

0,0,0cJ

bJ

aJ

6.3 Calculation of initial cutting tool posture It is determined which direction the cutting tool should approach from, and it is calculated how the attitude should be to cut the bone. For reasons of safety, a strategy of not changing the tool attitude has been adopted in the system, as shown in Figure 8. This means that the surgeon can predict the motion of machine tool easily, and the

1

2

3

(a) Femoral head (b) Posterior distal end

8 4

5 67

(c) Anterior distal end

1. Center of femoral head 2. Medial epicondyle 3. Lateral epicondyle 4. Intercondylar notch 5. Deepest point of groove 6. Posterior of intercondylar notch 7. Posterior point of lateral condyle 8. Posterior point of medial condyle

(d) Characteristic points for registration

Figure 5: Registration points for a femur.

12

43

(a) Medial malleollous (b) Tuberosity

5

Opening area

Opening area

Tibia

Femur

Figure 7: Measurement of opening area using an optical position sensor.

Opening area

Cutting tool

Interference area

Resection area

Requiredincision area

Cutting tool postureFigure 8: Cutting tool posture for minimal invasiveness.

(c) Insersion of PCL

1. Most medial point of medial malleous 2. Most lateral point of lateral malleous 3. Medial edge of tibial tuberosity 4. Lateral edge of tibial tuberosity 5. Insertion of PCL

(d) Characteristic points for registration

Figure 6: Registration points for a tibia.

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withdrawal of the tool in an emergency can be executed immediately. Utilizing the cross detection of the cutting tool vector and the target plane, the machinable area is calculated at a given cutting tool attitude, and a posture to maximize it without collision is selected. A local coordinate system is set on the opening area S measured with the 3-dimensional sensor. The normal direction is along the Z-axis and is defined as n. The resection plane is divided into the triangle patches Ki as shown in Figure 9(a), and vertex vectors are set qi. Tool vector with a attitude vector l and an offset vector from the origin p comes to p+ tl, and Equation (3) shows one of the triangle patches Ki (i=1, ...).

1 0 v 1 2 u,vuvu qqq 10 (3)

The following equation detects whether this patch is machinable [16].

00201 qpqqqql-vut

(4)

When it is machinable, the collision with the interferences Ti (i=1, ...) is checked next as shown in Figure 9(b). As expressed in Equation (5), the offset vector p is varied on the opening plane with the parameter of the tool attitude l,and the machinable area is calculated on the triangle patch Ki. Likewise, the machinable area is computed on other triangle patches. An attitude l to maximize the evaluation function Equation (5) is selected as the initial tool posture.

(5) nK

K

dxdyE1

)( )J( pl,l Syx p,,

)collisionwith (0)collisionwithout (1

),( plE

6.4 Collision avoidanceInterferences with prohibited tissues are checked, and when an interference is detected, it is avoided with a minimal change of the cutting tool attitude. In this case, the avoidance direction is equal to the normal vector of interference plane in Figure 10, and two rotational angles are controlled for it.

6.5 Toolpath generation Setting of the initial posture is realized by rotational axes close to the base of the developed machine tool. A redundant rotational axis close to the cutting tool is used for collision avoidance. The processes above decide the final toolpath.

7 7-AXIS BONE CUTTING MACHINE TOOL Figure 11 shows the developed bone cutting machine tool. The machine has the following features to cut the bone

precisely and safely with minimal invasiveness.

Figure 10: Collision avoidance.

Figure 11: Muti-axis bone cutting machine tool and an experiment using a cadaver.

(1) The machine has C-arm type structure. It provides adequate workspace and a view for a surgeon. (2) 3 translational axes (U, V and W axes) and 3 rotational axes (A, B and C axes) are implemented in the machine. The machine can set an arbitrary attitude of a cutting tool with the 3 rotational axes. This enables the avoidance of collisions with the surrounding tissues during the surgical operation, and minimizes invasiveness. (3) The role of each degree of freedom is clearly determined. This makes it easy for a surgeon to predict the motion of the bone cutting machine tool, and to operate it. The safety of the patient and the surgeon are assured.

O

q0

q1q2

K1

K2q3

n

nk

S

pl

O

q0

T1

q3

n

S

pl

T2

T3

(a) Resection area (b) Interference

Interference plan

Figure 9: Cross detection strategy.

(4) The axes of all rotational degrees of freedom intersect at the same point. Therefore, even when a posture change of the cutting tool is required, the other axes do not move. Consequently, bone cutting is performed safely and precisely. (5) The spindle is covered with a sleeve so that only the cutting tool tip contacts the bone surface. This avoids damage to the soft tissues when the cutting tool interferes with the surrounding tissues. The spindle mechanism also satisfies the requirements for irrigation and sterility. (6) The elevation axis (Z-axis) is implemented beneath the C-arm. This makes it possible to approach the patient with

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the cutting tool from an arbitrary bed height. This axis minimizes the required range of motion of the other axes, reduces the total machine weight, and improves the machine handling in the operation room. After adjusting the machine tool height, the cutting tool posture is set by the 3 rotational axes. The implant planes are cut by the interpolated motion of the U, V and W axes of the bone cutting machine tool, with the A-axis as a redundant axis. Using the extra degree of freedom, a cutting process like a windshield wiper of a car is realized.

8 EXPERIMENTAL RESULTS Cutting experiments with model and cadaveric bones were conducted using the developed system. In the experiment, the calculated toolpath for the minimally invasive surgery was applied. After the experiment, the bone surface was measured with a CMM to evaluate the position of the implant, comparing it with the planned position in the preoperational software. Table 1 shows the angular error of adjacent planes. The maximum error was 1.0 deg. and the geometric shape was well machined. Table 2 shows the measured implant position in the model bone cutting experiment. Distal plane of the implant is perpendicular to the load axis of femur. Posterior plane of the implant is parallel to SEA in the preoperational plan. The angle error was less than 2.0 deg. compared with the preoperational plan. It is less than the allowable error. A cadaveric experiment was also conducted using the developed system. The incision length was reduced from 150 mm to 100 mm.

9 CONCLUSIONS 1. A medical CAD/CAM system has been developed to

assist in minimally invasive knee arthroplasty. In particular, a method was proposed to measure the positions of soft tissues, like cutis and ligaments, and to avoid any collision with these obstacles. The system has a feature to provide safe operation by not changing the posture of the bone cutting machine tool during the surgical operation.

2. A multi-axis bone cutting machine tool with safety, sterilization and irrigation capability was implemented.

3. Cutting experiments for model bones were performed using the developed system. The angular error from the load axis of the femur was less than 2.0 deg. The maximum angle error of adjacent planes was approximately 1.0 deg. The incision length was

reduced to 100 mm in a cadaveric experiment.

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[2] ElMaraghy, H. and Yang, X., 2003, Computer-aided planning of laser scanning of complex geometries, Annals of the CIRP, 52/1:411-414.

[3] Kimura, F., Ariyoshi, H., Ishikawa, H., Naruko, Y. and Yamato, H., 2004, Capturing expert knowledge for supporting design and manufacturing of injection molds, Annals of the CIRP, 53/1:147-150.

[4] Noël, F., Brissaud, D. and Tichkiewitch, S., 2003, Integrative design environment to improve collaboration between various experts, Annals of the CIRP, 52/1:109-112.

[5] Galantucci, L.M., Percoco, G. and Spina, R., 2004, An artificial intelligence approach to registration of free-form shapes, Annals of the CIRP, 53/1:139-142.

[6] Morishige, K., Kase, K. and Takeuchi, Y., 1996, The Method of Collision Avoidance for 5-Axis Control Machining Using 2-Dimensional Configuration Space, Journal of JSPE, 62/1:80-84.

[7] Lauwers, B., Kiswanto, G. and Kruth, J.P., 2003, Development of a five-axis milling tool path generation algorithm based on faceted models, Annals of the CIRP, 52/1:85-88.

[8] Lartigue, C., Tournier, C., Ritou, M., and Dumur, D., 2004, High-performance NC for HSM by means of polynomial trajectories, Annals of the CIRP, 53/1: 317-320.

[9] Bürger, T., Laible, U. and Pritschow, G., 2001, Design and Test of a Safe Numerical Control for Robotic Surgery, Annals of the CIRP, 50/1:295-298.

[10] Joskowicz, L., Taylor, R., et al., 1995, Computer Integrated Revision Total Hip Replacement Surgery: Preliminary Report, MRCAS’95, 193-202.

[11] Rodriguez, F., Harris, S., Jakopec, M., Barrett, A., Gomes, P., Henckel, J., Cobb, J. and Davies, B., 2005, Robotic clinical trials of uni-condylar arthroplasty, Int J Medical Robotics and Computer Assisted Surgery, 1/4:20-28.

[12] Maillet, P., Nahum, B., Blondel, L., Poignet, P. and Dombre, E., 2005, BRIGHT, a Robotized Tool Guide for Orthopaedic Surgery, ICRA2005, 212-217.

Evaluated plane Planned (deg.) Measured (deg.) [13] Chung, J.H., Ko, S.Y., Kwon, D.S., Lee, J.J., Yoon, Y.S. and Won, C.H., 2003, Robot-assisted femoral stem implantation using an intramedulla gauge, IEEE Transaction on Robotics and Automation, 19/5:885-892.

95.5 1.0Anterior - Distal 95.0Distal - Posterior 90.0 90.1 1.0

[14] Plaskos, Ch., Cinquin, P., Hodgson, A.J. and Lavall e, S., 2005, Safety and Accuracy Considerations in Developing a Small Sterilizable Robot for Orthopaedic Surgery, ICRA2005, 942-947.

*Calculated value from 3 samples *Feed speed : 200 mm/min, Cutting depth : 2 mm

Table 1: Angle accuracy between two adjacent planes.

[15] Mitsuishi, M., Warisawa, S., Tajima, F., Suzuki, M., Tanimoto, K. and Kuramoto, K., 2003, Development of a 9 axes Machine Tool for Bone Cutting, Annals of the CIRP, 52/1:323-328.

Planned(deg.)

Measured(deg.)Evaluated plane

89.4 1.0Load axis / Distal 90.0 [16] Möller, T. and Trumbore, B., 1997, First, Minimum Storage Ray-Triangle Intersection, Journal ofGraphics Tools, 2/1:21-28.----------------------------------

SEA / Posterior 0.0 -0.2 2.0

[17] -Table 2: Orientation accuracy.