COMPARATIVE STUDY OF ROBOT-DESIGNS FOR A

HANDHELD MEDICAL ROBOT

Peter P. Pott, Markus L. R. Schwarz

Laboratory for Biomechanics and experimental Orthopaedics, OUZ, Medical Faculty Mannheim

University of Heidelberg, Theodor-Kutzer-Ufer 1-3, 68167 Mannheim, Germany

Achim Wagner, Essameddin Badreddin

Automation Laboratory, University of Mannheim, Mannheim, Germany

Keywords: Hybrid kinematics, Medical robotics, Comparison.

Abstract: Robotic systems are used within a great variety of medical disciplines. A handheld robot promises a number

of advantages compared to conventional (medical) robots but this approach leads to strict specifications

regarding size, weight and dynamic properties. A new hybrid kinematics – the Epizactor – seems to be

advantageous and is compared to two well-known parallel kinematics regarding the ratio of workspace and

volume the number of kinematic elements, the cost of computation, the stiffness the effects of clearance,

actuation (weight), and accuracy using a well-described industrial method for comparison. It becomes clear

that the Epizactor has advantages concerning the ratio of workspace and volume, needs a smaller number of

kinematic elements and fewer computations, and has less than half the mass than the parallel kinematics. Its

accuracy, stiffness and the effects of clearance are comparable. The advantages of this new kinematic set-up

lead to a first deployment within the field of medical robotics.

1 INTRODUCTION

Design and evaluation of robotic set-ups for medical

and especially surgical applications has been

ongoing for the last 20 years. Systems for a vast

variety of medical disciplines and deployments have

been investigated (Pott PP et al., 2005). One possible

solution to provide a useful tool for numerous

medical tasks is to use a handheld robot that

combines the process control of the surgical task by

the surgeon and the accuracy and repeatability of a

robot. Within the project "Intelligent Tool Drive"

ITD, a handheld robot for orthopaedic surgery is

being developed. The intention is to align a milling

tool relatively to a patient and to decouple the tool

from unintentional hand movements at the handle

(Pott PP et al., 2003; Wagner A et al., 2004). A

handheld robot has to be as small and lightweight as

possible while providing high dynamics for accurate

stabilisation of a surgical tool (Wagner A et al.,

2004). This most important criterion is mainly

determined by the kinematic set-up.

Figure 1: The EPIZACTOR, 6-DOF hybrid kinematics

with rotating elements.

Parallel robots are widely used, where high

stiffness, high dynamics, or low error propagation

103

P. Pott P., L. R. Schwarz M., Wagner A. and Badreddin E. (2008).

COMPARATIVE STUDY OF ROBOT-DESIGNS FOR A HANDHELD MEDICAL ROBOT.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - RA, pages 103-110

DOI: 10.5220/0001494001030110

 SciTePress

over the kinematic chains is required, e.g.

positioning and stabilization platforms (Huynh P,

2001) and vibration isolation (Chen Y et al., 2004).

An obvious advantage is that a parallel robot

provides high potential for a lightweight

construction. The moving masses of parallel

kinematics are low and this leads to low static and

dynamic forces (Honegger M, 1999; Huynh P,

2001).

Figure 2: The HEXAPOD, 6-DOF parallel kinematics

with actuated prismatic joints in the struts.

Alternatively a new kinematic set-up can be used

(). This concept –called "Epizactor"– involves two

disk-systems (systems A&B) each described by a

planar 3-DOF 4-link manipulator. These two serial

kinematic chains act on a connecting element that

moves the surgical tool by homokinetic joints with a

lead-screw and a prismatic section respectively.

Each disk-system uses four links to overcome

singularities by redundancy. So this hybrid

kinematics uses only rotating elements to provide 6-

DOF manoeuvrability (Pott PP et al., 2007; Pott PP,

Weiser HP et al., 2004).

The aim of this work is the comparison of a new

kinematic set-up with two well-known alternatives

for a handheld medical robot.

2 MATERIAL & METHODS

Three different kinematic set-ups were assessed. The

well-known Stewart-Gough-platform or Hexapod

(Figure 2) with active struts (Gough V et al., 1962;

Stewart D, 1965), the Merlet-platform or Hexaglide

(Merlet JP, 1988) with base-fixed actuators and

passive struts (Figure 3) and the Epizactor (Pott PP

et al., 2007; Pott PP, Weiser HP et al., 2004) (). The

first two set-ups are based on parallel kinematics

while the Epizactor is based on a hybrid kinematics

set-up. To describe the set-ups' forward and inverse

kinematics as well as the inverse dynamic models a

literature research and own considerations were

conducted. For the assessment of the actual

mechanical design three robots were available. Each

is based on one of the kinematic set-ups described

and shows a certain state of project ITD.

2.1 Comparison

To compare the kinematic set-ups the method by

Kesselring (Kesselring F, 1951) is used. Here a set

of criteria is defined and evaluated by one or more

experts using a score reaching from 4 (very good) to

1 (poor). To further refine the comparison, each

criterion is weighted. Finally for each kinematic set-

up the sum of all products of score and weight are

added up and lead to a total benchmark for each

kinematic set-up. To define the weighting factors the

method described by Wenzel (Wenzel R et al., 1971)

is used. Here all criteria are listed and each criterion

is compared to the remaining leading to a graduation

in importance of the different criteria.

Figure 3: The HEXAGLIDE, 6-DOF parallel kinematics

with base-fixed actuates prismatic joints.

To assess the three kinematic set-ups the

following criteria were used.

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2.2 Ratio of Workspace and

Installation Space

Given a certain workspace needed for a specific

task, this ratio describes how large a machine will

become at least. Especially in a surgical

environment the installation space should be as

small as possible while the workspace is determined

by the surgical task.

To assess this ratio each kinematic set-up was

simulated using Matlab (The Mathworks Inc,

Natick, MA, USA) and a given workspace definition

of 40mm translation of the tool in each axis and

±20° rotation in each axis at all times. Using this

simulation procedure the three kinematic set-ups

were scaled until predefined kinematic restrictions

were just not violated but the desired workspace

could still be produced. Each kinematic set-up is

circumscribed by a cylinder that defines the minimal

installation space of an imaginary machine based on

the corresponding kinematics. The length of the

cylinder is aligned with the tool nearest to the base-

platform.

2.3 Number of Kinematic Elements

Kinematic elements are defined as "joints", "struts"

or "links", "base", and "tool". The number of

kinematic elements can be used as a measure of

complexity of a kinematic set-up (El-Shenawy A et

al., 2007).

To assess the number of kinematic elements each

kinematic set-up was analysed and the elements

were counted.

2.4 Cost of Computation

The cost of computation can be a measure for the

hardware-effort that has to be made by the control

system to compute the forward and inverse

kinematic problems in real-time.

To assess the cost of computation for each

kinematic set-up the Matlab-code was analysed

regarding the number of additions,

multiplications/powers and trigonometric functions.

To compare the three set-ups a computation of both

kinematic problems was concerned and all

computation steps were summed up. The set-up with

greatest number was rated "1" the one with the

smallest number was rated "4". In between a linear

interpolation was performed.

2.5 Stiffness

Although stiffness is not a kinematic property and

system stiffness is mainly affected by the actual

design of a machine the three set-ups can be

analysed qualitatively regarding the distribution of

forces within the kinematic elements. It can be stated

that short and compact elements under uniaxial load

will be stiffer than flat elements under bending

strain.

To analyse the three set-ups the kinematic

elements were examined regarding the distribution

of force and shape.

2.6 Effects of Clearance

As it can be regarded as one of the major

impediments for accurate machine performance

clearance becomes one of the most important

criteria. Again this is not a purely kinematic feature

but the kinematic set-up has an influence on error

propagation.

To assess the effects of clearance a score

especially for the assessment of parallel and hybrid

kinematics was introduced (Pott PP, unpublished). It

was assumed that the clearance k

of i joints of a

serial kinematic chain in the most unfavourable case

is summed up to

∑

isertot

(1)

For the parallel arrangement of j serial chains it

is assumed that the clearance can be treated as

()

∑

serjpartot

(2)

For simplification the clearance in any joint is

standardised to "1".

2.7 Actuation / Weight

The actuation of a robot is not a kinematic property

but becomes important when size and weight of the

actual machine is evaluated. Electromagnetic linear

actuators provide high acceleration but a poor force-

to-weight ratio. Correspondingly conventional

COMPARATIVE STUDY OF ROBOT-DESIGNS FOR A HANDHELD MEDICAL ROBOT

105

rotating motors deliver high power at high speeds

but poor torque when used without gearing (Pott PP,

unpublished). So the actuation has an immanent

influence on the weight of a machine based on a

certain kinematic set-up.

To assess the three kinematic set-ups they were

analysed regarding performance needed and

theoretical weight. To determine the strut forces of

the Hexapod and the Hexaglide corresponding

dynamic models were used (Dasgupta B et al., 1998;

Khalil W et al., 2004; Wagner A et al., 2006).,

dynamic models (Dasgupta B et al., 1998) were

used. The Epizactor was assessed using a model

based on the iterative Newton-Euler-Method and

own considerations regarding the forward- and

inverse kinematic problems (Pott PP et al., 2007). As

input for the simulation a vibration trajectory with

12Hz and 1mm amplitude was used. This trajectory

was applied to each of a set of 680 pre-defined grid-

points throughout the whole desired workspace.

Additionally the direction of the trajectory and the

static forces

[]

202020=

and moments

[]

NmM

8.011=

were permutated in the main

coordinate system directions. Forces, moments,

frequency (velocity, acceleration) were taken from

the specifications of the handheld robot (Pott PP et

al., 2003; Pott PP, Wagner A et al., 2004). Masses

and mass-related values of the kinematic elements

were taken from the CAD-models of the three

available robots. The maximum forces and torques

in each actuator were computed. For the parallel

kinematics this force was multiplied by six, as the

symmetry of the set-up leads to the conclusion that

any actuator will have to be able to produce this

force. Regarding the Epizactor the torques of all

actuators were summed up. To achieve the

theoretical weight of the actuators of each set-up the

over-all force was multiplied with the specific force-

to-weight-ratio of the linear actuators and the

rotating actuators respectively. It could be shown

from manufacturer's data that an average electric

linear motor with a maximum force of about 50N

(30s) has a force-to-weight ratio of about 47.2N/kg.

The torque-to-weight ratio of an average motor with

a gear that allows a torque of 1Nm is about

3.4Nm/kg (Pott PP, unpublished).

2.8 Accuracy

The accuracy of a robot is determined by the

accuracy and resolution of sensors and actuators, the

adjustment of control parameters, the elastic

properties of the mechanics, and the transformation

of workspace coordinates into actuator axis

positions. As the first three parameters are affected

by the actual mechanical design, the latter is

dependent on the kinematics-type and actual

configuration only.

To assess the theoretical accuracy the tolerable

position error of the robot of 0.1mm (Pott PP et al.,

2003) was applied to the set of grid-points described

above. Doing so, the displacement of the actuators

was computed and compared to a realistic accuracy

of 0.005mm and 0.0005rad respectively, which can

be reached by real encoders used in a mechanical

design. A score was introduced that describes the

number of points where the accuracy specification is

reached.

3 RESULTS

3.1 Comparison

Table 1 shows a summary of the results for each

kinematic set-up. The comparison criteria are

aligned in rows. The columns show results, ratings

and weighted scores for each of the three kinematic

set-ups. The results of the comparison and a ranking

are summed up in the bottom line. It becomes clear

that the Epizactor has advantages regarding the ratio

of workspace and installation-space and theoretical

weight of its actuators. Additionally it needs less

kinematic elements, uses rotating actuators that

provide a better performance-to-weight ratio than

linear motors, and needs fewer computations for the

inverse and direct kinematic problem. Main

disadvantage of this new kinematic set-up is the

limited stiffness.

3.2 Ratio of Workspace and

Installation Space

The Hexapod can be enclosed by a cylinder with a

minimal volume of 3941cm³. This leads to a ratio of

workspace and installation space of 1:62.

The cylinder around the Hexaglide has a

minimal volume of 4247cm³ so the ratio of

workspace and installation space can be computed to

1:66.

A cylinder circumscribing the Epizactor has a

volume of 1445cm³. Compared with the required

workspace this leads to a ratio of workspace and

installation space of 1:23.

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3.3 Number of Kinematic Elements

The Hexapod and the Hexaglide each consist of a

base-platform, a tool-platform, and six legs. Each

leg uses two rotating and one prismatic (actuated)

joint and a strut. Overall 26 kinematic elements can

be counted.

The Epizactor consists of a base, a connecting

element (tool) and two identical disk-systems. Each

disk-system has 3 disks and a homokinetic joint. The

first disk is actuated directly. To drive the 2

disk a

single toothed ring is necessary, to drive the 3

disk

two toothed rings are used and the joint is driven by

three rings. Overall 22 kinematic elements can be

counted.

3.4 Cost of Computation

To calculate the Hexapod's inverse kinematic

problem 60 additions, 132 multiplications and

powers, and 174 trigonometric functions have to be

computed. The forward kinematic problem can only

be solved by an iterative procedure. Within the

simulations carried out around 40 iteration steps

were necessary for each computation. To compute

the kinematics once in both directions 15086

computations have to be carried out.

For the Hexaglide the inverse kinematic problem

is solved in the same way and also the forward

kinematics needs to be computed by iterations. Here

around 10 iteration steps were necessary. To

compute the kinematics once in both directions 4046

computation steps have to be done.

The inverse kinematic problem of the Epizactor

needs 106 additions, 171 multiplications and

powers, and 132 trigonometric functions. The

forward kinematics are computed by 31 additions,

115 multiplications and 177 trigonometric functions

(Pott PP, unpublished). To compute the kinematics

once in both directions 732 computations have to be

carried out. One has to consider that the inverse

kinematic problem finally is solved by a singularity-

robust control algorithm (Chung YG et al., 2000;

Pott PP et al., submitted) and does not need to be

computed.

3.5 Stiffness

The struts of the Hexapod kinematics can be

regarded as pendulum links. Each of the struts is

loaded by pressure and tension which must be fully

Table 1: Summary of the results and comparion of the three kinematic set-ups assessed. The comparion criteria are

aligned in rows, the results of the comparison, the rating, and weighted results are listed in columns. The bottom lines

show the result and the ranking of the three kinematic set-ups. The higher the result the better the set-up is suited for the

assessed deployment.

Hexapod Hexaglide Epizactor criteria unit weight

results rating result

rating

results rating result

rating

results rating result

rating

Ratio of

Workspace

and Instal-

lation Space

1 0.28 1:62 2 0.56 1:66 2 0.56 1:23 4 1.12

Number of

Kinematic

Elements

1 0.09 26 3 0.27 26 3 0.27 22 4 0.36

Cost of

Computa-

tion

score 0.02 15086 1 0.02 4046 3.36 0.07 732 4 0.08

Stiffness

rating 0.14

high and

constant

stiffness

4 0.56

high but

variable

stiffness

3 0.42

medium

stiffness

2 0.28

Effects of

Clearance

score 0.19 7.3 2 0.38 7.3 2 0.38 7.1 2 0.38

Actuation /

Weight

kg 0.19 7.1 1 0.19 5.6 2 0.38 2.2 4 0.76

Accuracy score 0.09 300 1 0.09 440 2 0.18 420 2 0.18

Results of

the compa-

rison

2.07 2.26 3.16

Ranking 3 2 1

COMPARATIVE STUDY OF ROBOT-DESIGNS FOR A HANDHELD MEDICAL ROBOT

107

absorbed by the actuated prismatic joint in each

strut. As the passive parts in each strut can be

designed as stiff as necessary the stiffness of the

prismatic joint depends on its design, the

construction of the actuator, and the quality of the

control loop. The stiffness of the struts is almost

constant over the length so it can be stated that the

over-all stiffness of the Hexapod in its workspace is

constant.

To consider the stiffness of the Hexaglide a

similar approach can be used. Differences exist as

the struts of the Hexaglide usually tend to be as light

as possible as they do not need to be actuated. Also

two variations of parallel kinematics with base-fixed

actuation exist. One that uses sliders (Hebsacker M

et al., 1998), here the over-all stiffness within the

workspace can be seen as constant. The version that

uses piston-like actuators (Merlet JP, 1988) provides

lower stiffness for extended actuators and changing

over-all stiffness within the workspace.

Forces applied to the connecting element of the

Epizactor are propagated to the disk-systems and

absorbed within the planes of the disk systems. The

stiffness of the disk-systems in this direction is

rather good. Only the force-component within the

axis of the connecting element acts perpendicular to

disk-system B so that here the stiffness is less good.

The stiffness is constant within the workspace as the

connecting element can be designed as stiff as

necessary.

3.6 Effects of Clearance

The Hexapod is based on six identical kinematic

chains between base-platform and tool. Each chain

consists of three joints. The clearance k

tot,ser

of each

chain is computed to

3111

=++==

∑

isertot

. (3)

For the whole set-up the score can be computed to

()

3.736

=⋅==

∑

serjpartot

(4)

The same assumptions can be made for the

Hexaglide and lead to a similar result.

The Epizactor uses two serial chains with 5

elements acting in parallel on the connecting

element. The clearance k

tot,ser

of each chain is

computed to

511111

=++++==

∑

isertot

. (5)

For the parallel arrangement of the two chains,

the overall score can be computed to

(

)

1.755

=+==

∑

serjpartot

. (6)

3.7 Actuation / Weight

The simulations for the Hexapod lead to maximum

forces of 55.7N in each strut. Thus the six actuators

needed to drive the Hexapod weighs at least 7.1kg.

For the Hexaglide the maximum force needed to

drive the set-up is 44.4N. With the same

considerations regarding the force-to weight-ratio

the actuators theoretically weigh about 5.6kg.

The Epizactor has a maximum torque

requirement in the specific actuators of 1.33Nm,

1.53Nm, 0.94Nm, 0.8Nm, 0.95Nm, 1.52Nm,

0.26Nm, and 0.02Nm. So the theoretical weight of

all actuators of the Epizactor sums up to 2.2kg.

3.8 Accuracy

The Hexapod can provide the desired kinematic

accuracy in 300 of the tested 680 grid-points. These

points are located near the main xz- and yz-plane of

the base-platform.

The Hexaglide reaches the desired accuracy in

440 of the tested grid-points. These are distributed

symmetrically to the main xz-plane of the base.

Within a small strip just next to this plane the

accuracy is not reached.

The Epizactor reaches the accuracy specification

on 420 grid-points. These are symmetrically

distributed within the workspace. The desired

accuracy is not reached at points were a certain

configuration of the disks leads to a very sensitive

behaviour of the kinematics.

4 DISCUSSION

Three different kinematic set-ups have been

evaluated. The method to compare the three

kinematic set-ups refers to the German norm VDI

2222. This method leads to a reproducible result

when it is done out by a group of experts. Here a

single expert carried out the comparison so a certain

bias can be assumed. However as primarily

measurable criteria were evaluated, the bias is

believed to be small. The graduation of the ratings is

rather raw but this simplifies the rating itself. It

becomes obvious that the Epizactor provides a

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108

number of advantages when compared to two well-

known parallel kinematic set-ups. This lead to the

decision to design such a set-up within the medical

robotics project ITD and for future projects.

It could be shown, that the ratio of desired

workspace and theoretical installation space of the

Epizactor is about three times better when compared

to the well-known parallel kinematics. The desired

workspace is derived from the specifications of the

ITD project and is described by a cube. If another

workspace-specification is taken into account, the

comparison will produce different results. The

method to simulate the desired workspace and to

scale down the kinematic set-up does not lead to an

optimization but seems to approximate the actual

set-up to this point. This criterion is the most

important within the comparison.

The Epizactor needs a smaller number of

kinematic elements than the Hexapod or the

Hexaglide. However the larger number of common

parts within the parallel kinematics simplifies the

actual manufacturing of those kinematic set-ups.

The fact that there seems to be no closed-form

solution for the inverse kinematics of the Hexapod

and the Hexaglide leads to a large number of

computations for the forward kinematic problem. In

contrast the mathematically well-defined kinematics

of the Epizactor leads to only a small number of

computations. It has to be considered that the code

analysed for comparison is not optimised. Although

the cost of computation is unequally distributed

between the three kinematic set-ups this criterion has

the least importance, as today's computer

performance allows even large computations in real-

time.

Stiffness is depending on the actual design of a

machine and is not an original kinematic property. It

is affected by the force distribution in the kinematic

set-up and therefore can be regarded quite important

as it applies to the robot's accuracy. Here stiffness is

analysed qualitatively and leads to the conclusion

that the Epizactor appears to be less stiff as forces

are distributed through flat rotating elements rather

than by robust pendulum supports utilised by the

parallel kinematics.

Although the effect of clearance is the second

most important due to accuracy reasons the

differences between the three set-ups are marginal as

it could be shown by the score that was introduced.

This can be explained by the fact that the length of

the kinematic chains and their quantity compensate

for each other. One has to remark that this score can

only be applied to parallel kinematics and that

experimental results have not yet been made to

substantiate this comparison.

While actuation is not a kinematic property this

criterion is used to evaluate a theoretical weight of

the actuators and hence for the weight of a

hypothetically realised machine. During the work on

the ITD-project it became obvious that linear

actuators seem to provide an unfavourable ratio of

force and weight, so that a machine driven by such

actuators becomes heavier than a machine driven by

rotating actuators considering comparable

performance. This also applies when rotating

spindles are used because of their additional weight.

The parallel kinematics are 3.2 times (Hexapod) and

2.5 times (Hexaglide) heavier than the Epizactor due

to the use of rotating actuators in this set-up and its

more favourable dynamic properties.

The resolution and accuracy of sensors for linear

displacement and rotating angles are limited. So the

accuracy of a machine based on a certain kinematic

set-up is not only limited by mechanical precision,

elasticity and the quality of the control loop but also

by the kinematic transformation of tool and axis

coordinates. The Epizactor's coordinate

transformation seems to be advantageous here.

The discrimination between purely kinematic

properties and features of the technical realisation is

not easy. This seems not to be a disadvantage as the

idea of the Epizactor aims to a practical use of the

kinematics in a handheld medical robot.

5 CONCLUSIONS

The Epizactor is a new kinematic concept for a small

6-DOF robot. A first deployment of this approach

will be a handheld robot for medical applications.

Here sharp restrictions regarding size, weight and

workspace exist and it could be shown, that the

Epizactor meets the main specifications in a most

favourable way.

ACKNOWLEDGEMENTS

The work on the ITD-project is supported by the

AiF, Berlin, Germany and has been supported by the

German Research Society. The work on the

Epizactor has been supported by the state of Baden-

Württemberg, Germany. The authors want to

express their most sincere gratitude to Prof. P.

COMPARATIVE STUDY OF ROBOT-DESIGNS FOR A HANDHELD MEDICAL ROBOT

109

Weiser and Mr. Steffen Heute who both contributed

greatly to the development of the Epizactor.

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