612 of the first cantilever beam 462 in a direction that is normal to the slave pivot axis 602, to urge rotation of the first cantilever beam 462 in a direction toward the second beam 464 to close the jaws.

A distal end portion of a second cable 614 that extends longitudinally within the hollow shaft 410 wraps about a perimeter groove portion of a second pulley (not shown) mounted to the clevis 606 in parallel with the first pulley 604. A proximal end (not shown) of the second cable 614 is operatively coupled to an actuator motor to impart a second cable force F_C2upon the second cable 614 to rotate the first beam 462 awayd the second beam 464 to ‘open’ the jaws. A distal end of the second cable 614 is secured to the first cantilever beam 462 such that a proximal direction second cable force F_C2exerted on the second cable 614 imparts causes the rotatably mounted first cantilever beam 462 to rotate in a direction away from the second beam 464 to open the jaws. In some embodiments the first and second cables 608, 614 include center segments that include elongated tubules and end segments that comprise wire.

During gripping of anatomical tissue 603, for example, a cable drive mechanism 458 described above, causes the first cable 608 to exert the first cable force F_Caxially upon the first cable 608 to a impart rotation force to the first cantilever beam 462 that balances a slave grip counter-force F_gripimparted to the working surface 612 of the first cantilever beam 462 by the gripped tissue 603. The grip counter-force F_gripbalances the first beam force first cable force F_C. The balanced first cable force F_Cand the grip force F_gripeach produce a grip moment about the slave pivot axis, M_griprepresented in the following formulation.

M
grip

=

F
grip

·
L

=

F
c

·
l

(
1
)

where L represents a distance from the point where the slave grip force F_gripis applied to the slave pivot axis, and I represents a distance from the first cable anchor 610, where the first cable 608 is secured to the first cantilever beam 462, and the slave pivot axis 602. Thus, during gripping of anatomical tissue 603, the first cable force F_Chas a magnitude to counter-balance the slave grip force F_grip.

FIG. 7 is an illustrative side view of the chassis 440 of the surgical instrument 26 of FIG. 4 suspended from a support beam 702 in accordance with some embodiments. The chassis 440 is secured to the proximal end portion 456 of the shaft 410 of the surgical instrument 26. A first end portion 704 of the support beam 702 is secured to the chassis 440 and a second end portion 706 of the support beam 702 is secured to a mechanical ground 708. The support beam has a longitudinal axis 710 (the beam axis) that extends between its first and second ends 704, 706. In some embodiments, a mechanical support arm 72 acts as the mechanical ground 708. The center axis 411 of the hollow tube 410 is normal to the support beam axis 710.

A strain sensor 712 contacts the support beam 702 and is configured to measure strain imparted to the support beam 702. In some embodiments, the strain sensor includes resistive strain gauge, optical fiber Bragg grating, piezoelectric sensor. Strain is a measure of the amount of deformation of a body, such as the support beam and the strain sensor 702, due to an applied force. More specifically, strain can be defined as the fractional change of length.

The mechanical ground 708 acts as a fixed reference structure that does not exhibit strain due to the cable force F_Cor a slave grip force F_grip.

A third pulley 714 is rotatably secured to the chassis 440. A proximal end portion of the first cable 608 wraps about a perimeter groove portion of the third pulley 714. A first cable drive mechanism 458a, which is secured to the mechanical ground 708, is configured to impart the first force F_Cupon the first cable 608. In some embodiments, the first cable drive mechanism 458a includes a motor driven rotatable spindle mechanically coupled to a proximal end portion of the first cable 608. The third pulley 714 and the first cable drive mechanism 458a are disposed at a vertical offset from each other relative to the support beam axis 702 such that a proximal segment 608a of the first cable 608 between them extends at an offset angle θ from the support beam axis 710. The first cable drive mechanism 458a may impart a first cable force F_Cto the offset angled first cable segment 608a to close the jaws. The first cable force F_Capplied to the offset first cable segment 608a results in a first cable offset force component F_Csin θ upon the support beam 702 that is parallel to the shaft axis 411 and normal to the support beam axis 710 and a first cable offset force component F_Ccos θ upon the support beam 702 that is perpendicular to the shaft axis 411 and that is parallel to the beam axis 710. In reaction to the first cable force components, the support beam 702 produces reactive normal and parallel beam forces R_Xand R_Z. The reactive beam force R_Z, which shall be referred to herein as F_z,PSC, the z-force measured on the system side, acts as a strain force applied at the first end 704 of the support beam 702. The strain force F_Zis imparted in a direction normal to the support beam axis.

It will be appreciated that the first cable force F_Cimparted by the first cable within the shaft in a direction normal to the support beam axis 710 is balanced by an equal and opposite proximal-direction end effector force F_C′ resulting in a net force of zero upon the beam due to forces imparted to first cable segments within the shaft. Outside the shaft, however, the offset angled first cable segment 608a exerts a net force F_Csin θ normal to the support beam and in response, the support beam produces an opposing reactive force F_Z.

A fourth pulley 716 is secured to the chassis 440. A proximal end portion of the second cable 614 wraps about a perimeter groove portion of the fourth pulley 716. A second cable drive mechanism 458b, which is secured to the mechanical ground 708, is configured to impart a second cable force F_C2upon the second cable 614 to open the jaws. In some embodiments, the second cable drive mechanism 458b includes a motor driven rotatable spindle mechanically coupled to a proximal end portion of the second cable 614. The fourth pulley 716 and the second cable drive mechanism 458b are disposed level with each other without a vertical offset between them relative to the support beam 702 such no net normal force is exerted by a level second cable segment 614a extending between the fourth pulley 716 and the second cable drive mechanism 458b. The strain force F_Zexperienced by the support beam 702 due to the offset angled first cable segment 608a is a reactive force imparted that balances the net first cable force F_Csin θ imparted to the support beam 702. The strain force F_Zimparts a strain to the support beam 702 and to the strain sensor 712. The relationship between the net normal force F_Csin θ and the strain force F_Zimparted to the strain sensor 702 is represented by the following formulation (2).

F

z
,
PSC

=

F
c

⁢
sin
⁢
θ

+

F
cd

-

F
cp

=

F
c

⁢
sin
⁢
θ

=

M
grip

l

⁢
sin
⁢
θ

(
2
)

The strain sensor produces a sensor signal S_Sthat has a magnitude indicative of the magnitude of the strain force F_Z,PSC, which in turn is proportional to a magnitude of the grip moment M_gripabout the slave pivot axis, M_grip. In some embodiments, the signal may be a change in voltage on a Wheatstone bridge (not shown) produced by a resistance change on a strain gauge.

FIG. 8 is an illustrative free body diagram to show forces upon the grip members of a master control input and a surgeon's fingers in accordance with some embodiments. During a surgical procedure, a surgeon's fingers are placed on outside grip surfaces of the first and second grip members 530a, 530b. The first and second grip members 530a, 530b have proximal ends 530ap, 530bp and distal ends 530ad, 530bd. The distal ends 530ad, 530bd of the first and second grip members are pivotally mounted to pivot about the master pivot axis 536 and are offset from each other by an angle α. A surgeon's fingers 802a, 802b may apply fingertip forces to the first and second grip members 530a, 530b to move them along the firs path 850 about the master pivot axis 536, to move them closer together or farther apart so as to command corresponding movements of the first and second cantilever beams 462, 464 of the end effector 454. Specifically, for example, moving the proximal ends 530ap, 530bp of the first and second grip members 530a, 530b in a direction along the first path 850 to bring them closer together, which reduces the angle α between them, causes the first and second cantilever beams 462, 464 to move closer together, closing the end effector jaws. Conversely, for example, moving the proximal ends 530ap, 530bp of the first and second grip members 530a, 530b in an opposite direction along the first path 850 to space them farther apart from each other, which increases the angle α between them, causes the first and second cantilever beams to move farther apart, opening the end effector jaws. U.S. Pat. No. 6,594,552, which is incorporated in its entirety by this reference above explains grip member control of end effectors in accordance with some embodiments. Thus, the angle α between the distal ends 530ad, 530bd of the first and second grip members determines the positions of the corresponding first and second cantilever beams at the end effector.

More particularly, a bias member, such as a bias spring 804, provides a bias force F_springto urge the first and second grip members 530a, 530b away from each other. A surgeon may apply forces −F_N, which are normal to longitudinal axes 806a, 806b of the first and second grip members 530a, 530b. The surgeon-applied force −F_Nrotates the first and second grip members along the first path 850 about the master pivot axis 533 to bring their proximal end portions 530ap, 530bp closer together, reducing the angle α, between them, and commanding the imparting of the first cable force F_Cto cause the first and second cantilever beams 462, 464 at the end effector 454 to move closer together. Additionally, the surgeon's fingers 802a, 802b may impart surface forces −μ_SF_N, which are parallel to surfaces of the first and second grip members 530a, 530b, in combination with the surgeon-imparted normal forces −F_N.

The first and second grip members 530a, 530b impart opposite direction normal forces F_Nto the surgeon's fingers 802a, 802b in reaction to the surgeon-imparted normal forces −F_N. The first and second grip members 530a, 530b also impart opposite direction surface forces μ_SF_Nin reaction to the surgeon-imparted surface forces −μ_SF_N.

Thus, in accordance with some embodiments, the first and second cantilever beams 462, 464 correspond to the first and second grip master members 530a, 530b. Larger scale motions imparted by a surgeon's fingers to the master members 530a, 530b are translated to corresponding smaller scale motions of the first and second cantilever beams 462, 464. In particular, in accordance with some embodiments, for example, a rotation of the master members 530a, 530b about the master pivot axis 536 is translated to corresponding rotation of the first and second cantilever beams 462, 464 about slave pivot axis 602. In some embodiments, for example, translation of movement of the master members 530a, 530b translates to corresponding movement of the first and second cantilever beams 462, 464 such that an angle α about the master pivot axis 536 between the master members 530a, 530b matches an angle α slave pivot axis 602 between the first and second cantilever beams 462, 464. It is noted that during routine operation, the surgeon imparted forces and the grip member reaction forces are balanced. During routine operation, a friction force at the grip members 530a, 530b is static friction, which is just enough to match the parallel surface forces applied by the surgeon's fingers 802a, 802b at the grip members. It will be appreciated that reaction surface forces μ_SF_Nare less than a maximum permitted surface friction force F_frat which the grip members 530a, 530b start sliding in the surgeon's fingers 802a, 802b, causing the surgeon's finger's to lose their grip, at which point the surgeon may need to apply an increased normal force to increase the surface friction to stop the sliding. The relationship between surface force μ_SF_Nand maximum permitted F_fris represented by the following formulation.

F

fr
,
max

=

μ
s

⁢

F
N

(
3
)

In operation, a moment imparted by a surgeon 18 at distance a D from the master pivot axis 536 equals and is balanced by a moment imparted by the bias spring 804 at a distance d from the pivot axis 536. If it is assumed that a torsional spring has a spring force in indicated in the formulation.

F
spring

=

k
⁡
(

α
0

-
α

)

(
4
)

where k is the spring constant.

If it is assumed that α₀is the initial angular position, then the normal force F_Nis directly related to the angle α by the moment balance the following formulation.

F
N

⁢
D

=

F
spring

⁢
d

=

k
⁡
(

α
0

-
α

)

⁢
d

(
5
)

Thus
,

F
N

=

k
⁡
(

α
0

-
α

)

⁢
d

D

(
6
)

In view of equation (6), it will be appreciated that normal force F_Ncannot be modulated directly to display the grip force to the surgeon without changing the α, which would be detrimental to performance since it would affect the gripping angle of the first and second cantilever beams 462, 464 at the end effector 454. However, the inventor herein realized that a feedback surface force F_Z,MTMimparted to mount member 530, and through it, to the first and second grip members 530a, 530b mounted thereon, along a second path 852 in a direction toward the pivot axis 533 and toward a palm 808 of the surgeon's hand may be modulated to increase a surface feedback force imparted to the fingers 802a, 802b to thereby display an indication of a magnitude of the grip force moment M_gripat the end effector 454.

An upper limit of the feedback force F_Z,MTMis dependent on the amount of force required to make the grip members slip against the surgeon's fingers by overcoming static friction:

F

z
,
MTM

≤

2
·

(

F
N

⁢
sin
⁢
α

+

F

fr
,
max

⁢
cos
⁢
α

)

=

2
·

(

F
N

⁢
sin
⁢
α

+

μ
s

⁢

F
N

⁢
cos
⁢
α

)

(
7
)

F

z
,
MTM

≤