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Comparative analysis of RCM mechanisms based on parallelogram used in surgical robots for laparoscopic minimally invasive surgery

Trochimczuk Roman

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 4

911--925

EN

This article presents results of comparative analysis of kinematics and dynamics of five varieties of the parallelogram-based RCM mechanism applied in real-life designs of surgical robots. Analyses were conducted using ANSYSWorkbench v. 16.2. Obtained results allow for formulation of guidelines concerning conscious selection of the form of the RCM mechanism and assessment of its usefulness from the perspective of application in new solutions of laparoscopic surgical robots.

2

Finding Shortest Triangular Path and its Family inside a Digital Object

Sarkar A., Biswas A., Dutt M., Mondal S.

Fundamenta Informaticae

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2018

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Vol. 162, nr 1

73--100

EN

This article presents a combinatorial algorithm to find a shortest triangular path (STP) between two points inside a digital object imposed on triangular grid that runs in O(n/g log n/g)time, where n is the number of pixels on the contour of the object and g is the grid size. Initially, the inner triangular cover which maximally inscribes the object is constructed to ensure that the path lies within the object. An appropriate bounding parallelogram is considered with those two points in diagonally opposite corners and then one of the semi-perimeters of the parallelogram is traversed. Certain combinatorial rules are formulated based on the properties of triangular grid and are applied during the traversal whenever required to shorten the triangular path. A shortest triangular path between any two points may not be unique. Another combinatorial algorithm is presented, which finds the family of shortest triangular path (FSTP) (i.e., the region containing all possible shortest triangular paths) between two given points inside a digital object and runs in O(n/g log n/g) time. Experimental results are presented to verify the correctness, robustness, and efficacy of the algorithms. STP and FSTP can be useful for shape analysis of digital objects and determining shape signatures.

3

Finding Shortest Triangular Path and its Family inside a Digital Object

Sarkar A., Biswas A., Dutt M., Mondal S.

Fundamenta Informaticae

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2018

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Vol. 159, nr 3

297--325

EN

This article presents a combinatorial algorithm to find a shortest triangular path (STP) between two points inside a digital object imposed on triangular grid that runs in O(n/g log n/g) time, where n is the number of pixels on the contour of the object and g is the grid size. Initially, the inner triangular cover which maximally inscribes the object is constructed to ensure that the path lies within the object. An appropriate bounding parallelogram is considered with those two points in diagonally opposite corners and then one of the semi-perimeters of the parallelogram is traversed. Certain combinatorial rules are formulated based on the properties of triangular grid and are applied during the traversal whenever required to shorten the triangular path. A shortest triangular path between any two points may not be unique. Another combinatorial algorithm is presented, which finds the family of shortest triangular path (FSTP) (i.e., the region containing all possible shortest triangular paths) between two given points inside a digital object and runs in O(n/g log n/g) time. Experimental results are presented to verify the correctness, robustness, and efficacy of the algorithms. STP and FSTP can be useful for shape analysis of digital objects and determining shape signatures.

4

Banach-Mazur distance between convex quadrangles

Lassak M.

Demonstratio Mathematica

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2014

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Vol. 47, nr 4

989--993

EN

It is proved that the Banach–Mazur distance between arbitrary two convex quadrangles is at most 2. The distance equals 2 if and only if the pair of these quadrangles is a parallelogram and a triangle.