medical robotics kinematic design: examplesvenditt/didattica/mr/11_kinexamples.pdf · m....

$: Medical Robotics Kinematic Design: Examplesvenditt/didattica/mr/11_KinExamples.pdf · M. Vendittelli Medical Robotics (Universit a di Roma \La Sapienza") { Kinematic design: examples2$
Universita di Roma “La Sapienza”

Medical Robotics

Kinematic Design: Examples

Marilena Vendittelli

Dipartimento di Ingegneria Informatica, Automatica e Gestionale

April 10, 2017

example 1: design of an active heart stabilizer• traditional approach to cardiac surgery: the heart is stopped and an extracorporeal

circulation (ECC) is activated

• beating heart surgery can avoid harmful effects of ECC (e.g., stroke, neurologicalimpairment, vessel damage)

• a mechanical stabilizer is necessary to reduce the motion of the area interested by theprocedure

• passive stabilizers exhibit residual motions of the order of mm

• the required precision is of the order of 0.1 mm

invasive stabilizer Octopus 4.3 (Medtronic) endoscopic stabilizer Octopus TE (Medtronic)

M. Vendittelli Medical Robotics (Universita di Roma “La Sapienza”) – Kinematic design: examples 2

• the procedure is even more challenging if executed in a MIS context

⇒ use an active stabilizer to compensate for heart motion


active stabilizer kinematics

• two end-effector degrees of freedom in directions perpendicular to the stabilizer beam

• a RCM to limit the influence of the trocar forces

• the end-effector displacements needed to compensate for deflections are in the order of1–2 mm ⇒ L = 250 mm (length of the stabilizer allowing a correct access to the areaof interest) enables to approximate the needed device displacements by two rotationswith respect to the RCM

• the rotations of the stabilizer beam are of small amplitude ⇒ the special arrangementrepresented in the figure allows to get a decoupled behavior


jacobian matrix that relates the joint velocities (θ1 θ2)T to the end-effector velocities (x, y)

(xy

)=

(L sin(α1) 0

0 L sin(α2)

)(θ1

θ2

)

• in principle, for a given set of end-effector displacements, the required displacementsof the actuated joints decrease when angles α1 and α2 increase

• from a dynamical point-of-view, parameters α1 and α2 should be minimized in order toobtain a more compact structure, with lower inertias

actuation of joints J1 and J2

• stack piezo actuators do not introduce any backlash or friction but deliver linear motion⇒ an actuation stage has to be designed in order to transform this motion in a rotationof the joints of the serial spherical architecture

• to lower the angles α1 and α2 a high ratio rotation/translation is needed

• a slider-crank mechanism does not allow to increase rotation/translation ratio withoutreducing stiffness in certain directions

• parallel architectures can provide at the same time a stiff structure, to minimize anyuncontrollable displacements, and a large rotation from the displacement provided bythe piezo actuator


relationship between actuator velocities q and end-eff. velocities X for a parallel mechanism

Jq q = JX X (∗)

• in a singularity, where JX is not full rank, X 6= 0 can be obtained with q = 0

• in the vicinity of that singularity, one can tend to increase the ratio between actuatorsand end-effector velocities

• a 3-PRR in a configuration close to singularity provides the equivalent of a revolutejoint; the thickness of this planar parallel structure can be selected to obtain the desiredout-of-plane stiffnesses


• the pose of the end-effector X = (x, y, θ) is determined by its orientation θ and by theposition (x, y) of the point E

• the expression of Jq and JX can be easily derived by noting that the velocities vAiand

vBiof points Ai and Bi, respectively, satisfy the equality

vAi·AiBi = vBi

·AiBi

relating the velocities of any two points Ai and Bi of a rigid body (known as equipro-jective peoperty)

• in this case vAi= qiui, vBi

= vEi+ BiE × θ, (i = 1, 2, 3) which can be rewritten in the

matrix form (∗), with

Jq =

u1 ·A1B1 0 0

0 u2 ·A2B2 0

0 0 u3 ·A3B3

JX =

A1B1|x A1B1|y A1B1 ×B1E|θ



• if we consider zero velocities for the mechanism legs 1 and 3, the end-effector velocity(x, y) is zero

• the velocity q2 of the actuator 2 is linked to the rotational speed θ as

θ =1

||EB2|| sin(ε)q2


• the parallel structure is equivalent to an actuated revolute joint

• the ratio between the velocity q2 and θ can be easily tuned by changing the parameterε to obtain a high rotation/translation ratio

• the structure has interesting stiffness properties when forces in the plane of the mech-anism are considered

• out-of-plane stiffness is controlled by the width of the mechanism

Cardiolock2: a serial spherical architecture, each actuated revolute joint being obtained bymeans of a planar parallel structure in a configuration close to parallel singularity

• the parallel structures are controlled with piezo actuators and designed as compliantmechanisms

• the Pseudo Rigid Body Model (PRBM) approach allows to use the previous kinematicanalysis


example 2: image stabilization for in vivo microscopy

• molecular imaging is a novel technology that visualizes the functions of biologicalprocess at the cellular and molecular level within living organism

• confocal microscopy, which is categorized into optical molecular imaging, could havea substantial impact on molecular imaging in that it can provide very high spatialresolution to submicrometers

• small in vivo motion due to heartbeat and breathing makes microscopic observationdifficult by blurring the microscope image or impossible by sending a region of interestout of view


stabilization technology virtually removing the disturbing motion during observation


2 dofs Pentagon

• a piezoactuator-driven mechanical device

• transfers the movement of actuators to the movement of the objective lens and am-plifies the insufficient strokes of the actuators

• two piezoactuators push linkages l1 and l2

• the mechanism should have: 1) sufficient enlargement ratio; 2) more isotropic enlarge-ment

• these two properties can be obtained through the jacobian matrix Jrob relating the e.e.velocity to actuated joints velocities

r = JrobθG


• enlargement ration is obtained through the eigenvalues of Jrob

• more isotropic enlargement is obtained by maximizing the min singular value of Jrob

• to determine Jrob the closed chain is transformed into an equivalent tree structure byvirtually cutting some joints in closed loops

• the closed loop imposes the constraint that the velocity of the left link computed fromθ1 and θ3 should be equal to that of the right link from θ2, θ4 and θ5

r =(J1 J3

)( θ1

θ3

)=(J2 J4 J5

) θ2

θ4

θ5

where Ji = ∂r

∂θi

• dividing this equation into actuated and unactuated joints

JSθs = −JGθGwith θs = (θ3 θ4 θ5)T , JS = (J3 − J4 − J5), JG = (J1 − J2)

• the unactuated joints can be obtained as

θS = −J#S JGθG


• providing

r =(J1 J3

)( θ1

θ3

)=(J1 J3

)( 1 0JA

)(θ1

θ2

)where JA is the first row of −J#

S JG

• thus

Jrob =(J1 J3

)( 1 0JA

)• Jrob is a function of the link lengths and the joint angles; roughly as the total length of

linkages increases, the enlargement ratio increases, but the resonant frequency, whichdetermines the mechanical response, decreases

• a tradeoff has been found through an optimization procedure

• Pentagon amplifies the strokes of two actuators, 180 µm (Physik Instrumente: P-239.90, stroke 180 µm) to 563 µm and 464 µm, respectively

Bibliography

W. Bachta, P. Renaud, E. Laroche, J. Gangloff, “The Cardiolock Project: Design of anActive Stabilizer for Cardiac Surgery,” Journal of Mechanical Design, vol. 133, 2011.

S. Lee, Y. Nakamura, K. Yamane, T. Toujo, S. Takahashi, Y. Tanikawa, and H. Takahashi“Image Stabilization for In Vivo Microscopy by High-Speed Visual Feedback Control,” IEEETransaction on Robotics and Automation, vol. 24, no. 1, 2008.


medical robotics kinematic design: examplesvenditt/didattica/mr/11_kinexamples.pdf · m....

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