Methods for improving stability of concentric tube steerable devices using asymmetric flexural rigidity

A concentric tube steerable device comprising:

• an outer tube, wherein the outer tube comprises:
• precurved portion, wherein the precurved portion is defined by an axis of precurvature,
• a first plurality of discrete openings distributed along a first side of the outer tube, and
• a second plurality of discrete openings distributed along a second side of the outer tube, wherein the second side is opposite the first side,
• wherein the first plurality of discrete openings and the second plurality of discrete openings introduce asymmetric stiffness properties in the outer tube including a reduction in a flexural rigidity of the outer tube along the axis of precurvature relative to a flexural rigidity of the outer tube along a second axis that is perpendicular to the axis of precurvature, wherein a ratio of the flexural rigidity of the outer tube along the axis of precurvature to the flexural rigidity of the outer tube along the second axis is less than 0.8;
• an inner tube that is nested and extends coaxially within the outer tube, the inner tube terminating at a distal tip, wherein a pose of the distal tip is effectuated through individual or collective rotation or translation of the outer tube and/or the inner tube,
• an actuator for rotating at least one of the outer tube about an outer tube axis or the inner tube about an inner tube axis;
• and
• a translator for translating at least one of the outer tube along the outer tube axis or the inner tube along the inner tube axis.

A concentric tube steerable device, comprising:

• a plurality of tubes having a nested, concentric configuration, the plurality of tubes comprising an outer tube and an inner tube that extends coaxially within the outer tube, wherein the inner tube terminates at a distal tip, wherein a pose of the distal tip is effectuated through individual or collective rotation or translation of the plurality of tubes about a tube axis;
• and
• at least one actuator for rotating at least one tube of the plurality of tubes about a respective tube axis and/or translating at least one tube of the plurality of tubes along a respective tube axis,
• wherein each tube of the plurality of tubes comprises a precurved portion and corresponding axis of precurvature,
• wherein for each tube of the plurality of tubes:
• a flexural rigidity of a respective tube along its axis of precurvature is less than a flexural rigidity of the respective tube along a second axis that is perpendicular to the axis of precurvature, and
• a ratio of the flexural rigidity along the axis of precurvature squared over a torsional rigidity of the respective tube times the flexural rigidity along the second axis is less than a sum of 1 plus an effective Poisson's ratio of a material of the respective tube.