Triangle Parallel Research Articles

Comparison of the efficacy of TiRobot orthopaedic robot assisted F screw technique and inverted triangle parallel nail internal fixation in the treatment of unstable femoral neck fractures

To compare the effectiveness of TiRobot assisted F screw technique and inverted triangle parallel nail internal fixation in the treatment of unstable femoral neck fractures. A retrospective analysis was conducted on 72 patients with unstable femoral neck fractures who were treated with percutaneous cannulated screw fixation assisted with TiRobot Orthopaedic robot from December 2019 to April 2021. Among them, 37 patients were treated with F screw internal fixation, including 16 males and 21 females, aged 47 to 64 years old with an average of （53.87±5.28） years old；According to Pauwels classification, there were 1 case of type Ⅰ, 19 cases of type Ⅱ, 17 cases of type Ⅲ；8 cases of combined medical diseases；17 cases of falling, 8 cases of traffic accident and 12 cases of falling from height；The time from injury to operation was 29 to 49 hours with average of （35.00±7.34） hours. Another 35 cases used internal fixation with an inverted triangle parallel nail, including 13 males and 22 females with an average age of 46 to 63 years old （52.36±5.05） years old；According to the Pauwels injury classification：there were 2 cases of type Ⅰ, 21 cases of type Ⅱ, 12 cases of type Ⅲ；6 cases of medical diseases, 15 cases of falling injury, 9 cases of traffic accident, 11 cases of falling injury；The time from injury to operation was 30 to 45 hours with an average of （33.00±6.83） h. The intraoperative blood loss, operation time, intraoperative fluoroscopy times, follow-up time, fracture healing time, postoperative complications were observed and compared between the two groups. The hip joint function was evaluated by Harris score at 6 months and 12 months after operation. There was no significant difference in operation time, intraoperative blood loss, intraoperative fluoroscopy times and other intraoperative data between two groups（P>0.05）. Both groups were followed up regularly, and the follow-up time was 12 to 16 months. The fracture healing time and Harris score of the F screw internal fixation group were better than those of the inverted triangle parallel nail internal fixation group （P<0.05）. There was 1 case of femoral neck shortening in the F screw internal fixation group, 1 case of nonunion, 1 case of nail withdrawal, and 1 case of lower extremity deep vein thrombosis in the inverted triangle internal fixation group. The incidence of complications in the F screw internal fixation group was lower than that in the inverted triangle parallel nail internal fixation group（P<0.05）. Percutaneous cannulated F screw technique using Tirobot navigation positioning system is a safe and effective treatment for patients with unstable femoral neck fractures. It can significantly shorten the fracture healing time, reduce the incidence of postoperative complications, significantly improve hip joint function, and improve the quality of life.

HZ-Coindex for the Sum-Graphs under Cartesian Product

:Let G = (V (G), E(G)) be a simple connected graph with V (G) and E(G) as the vertex and edge sets respectively. The physical and structural properties of the graphs are discussed with different mathematical tools, One of them is topological index (TI) and it can be obtained directly from molecular structures and rapidly computed for large number of molecules. Graph operations play an important role in the development of various new classes of graphs. If G is a connected simple graph then we obtained new graphs by applying various operations on G such as S subdivided, R triangle parallel, Q line superposition and T total graphs operations on G. In this paper, we computed the hyper Zagreb coindex of derived graphs in the form of their factor graphs. At the end, we have analyzed our results by the numerical tables for the particular generalized D-sum graphs

Forgotten Coindex for the Derived Sum Graphs under Cartesian Product

A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H . For D ∈ S , R , Q , T and the connected graph H , the derived graphs D H are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph ( D -sum graph) is obtained by the Cartesian product of the graph H 2 with the graph D H 1 . In this study, we compute forgotten coindex of the D -sum graphs H 1 + S H 2 ( S -sum), H 1 + R H 2 ( R -sum), H 1 + Q H 2 ( Q -sum), and H 1 + T H 2 ( T -sum) in the form of various indices and coindices of the factor graphs H 1 and H 2 . At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D -sum graphs.

General Triangle Parallel Robot (GTPR) Basic Features of a New Robot Type - Kinematics and related Application Issues

General Triangle Parallel Robot (GTPR) Basic Features of a New Robot Type - Kinematics and related Application Issues

Four cannulated screws in self-designed configurations for fixation of extremely unstable femoral neck fractures: a biomechanical analysis

Objective To investigate the biomechanical properties of our self-designed 4 cannulated screws in 4 configurations for fixation of extremely unstable femoral neck fractures. Methods Twelve adult cadaveric femoral specimens were randomly divided into 4 equal groups (n=3) and made into models of extremely unstable femoral neck fracture combined with comminution (Pauwels type Ⅲ). Group A was subjected to fixation in configuration of axial compressions plus double stabilizations , group B to configuration of positive triangle parallel compression plus small angle screwing , group C to configuration of inverted triangle parallel compression plus small angle screwing , and group D to configuration of diamond pattern screwing . Static compression tests, cyclic loading tests and limit load tests were carried out for the 4 groups on a biomechanical testing machine. Results For groups A, B C and D, the axial compression stiffness was respectively 995.29±34.16 N/mm, 509.89±138.90 N/mm, 559.28±111.25 N/mm and 610.18±232.35 N/mm, and the limit load was respectively 3, 225.33±461.31 N, 2, 008.67±237.27 N, 2, 705.67±496.39 N and 2, 395.33±403.71 N, showing significant differences between the 4 groups (P 0.05). Conclusions In the fixation of extremely unstable femoral neck fracture with our self-designed 4 cannulated screws, the configuration of axial compressions plus double stabilizations may lead to the greatest biomechanical advantage while the configuration of positive triangle parallel compression plus small angle screwing may result in the poorest biomechanical properties. Key words: Femoral neck fractures; Fracture fixation, internal; Bone nails; Biomechanics

Analysis of Workspace and Singularity of a Slide Equilateral Triangle Parallel Manipulator

This paper presents a novel architecture of six-degree-of-freedom (6-dof) parallel manipulator. The parallel manipulator consists of a moving platform, a fixed base, and six supporting constant-length limbs. Since the structure of parallel manipulator is a double equilateral triangle, it is called a slide equilateral triangle parallel manipulator (SETPM). The inverse and forward kinematics problems are described in closed forms and the velocity equation of the new parallel manipulator is given. Three kinds of singularities are presented. In determining the workspace of the manipulator, four types of kinematic constraints have been taken into account. The parallel manipulator has compact configuration and no singularities existed in the workspace. A prototype parallel manipulator was built base on the kinematics and analysis results.

A real-time NURBS motion interpolator for position control of a slide equilateral triangle parallel manipulator

This study presents a real-time non-uniform rational B-spline (NURBS) motion interpolator command generation for position control of a new design to achieve a six-degree-of-freedom (6dof) slide equilateral triangle parallel manipulator (SETPM). The existing method utilizes the approximate method to obtain the characteristics of curves of the velocity and acceleration for the feed-forward compensation in the joint space. However, the NURBS motion interpolator command generation is related to the geometric characteristics of curves including position, tangent, and curvature to the motion dynamics of the SETPM including position, velocity and acceleration for applied directly the feed-forward compensation in the global space. The inverse dynamics controller (IDC) is the power of control law. However, implementing the inverse dynamics control laws requires accurately knowing the system dynamic model parameters and computing the complete equations of motion in real time. To reduce the time for calculating the inverse dynamic, this study proposes a feed-forward compensation with feedback proportional derivate (PD) control to take the place of inverse dynamics control for reducing both the inverse dynamic calculation time and the tracking error. The proposed real-time NURBS motion interpolator command generation and feed-forward compensation with feedback PD control are also successfully applied to a slide equilateral triangle parallel manipulator on a PC-based system to achieve high motion precision.

The structure of para-xylene and meta-xylene adsorbed on Rh(111) studied by scanning tunneling microscopy

Scanning tunneling microscopy (STM) was used to study the adsorption of para- and meta-xylene on the Rh(111) surface. Para-xylene appears in the STM images as a diamond-shaped feature with the long axis oriented along the [11 2 ] and equivalent directions. Ordered domains with three orientations differing by 120° are formed. The images of the meta-isomer have the appearance of triangular shapes and do not form any ordered structure. Individually, however, they are oriented with one side of the triangle parallel to the compact [1 1 0] directions. The internal structure in the molecular images can be discerned. By a combination of symmetry and packing considerations, it is possible to attribute the brightest part of the molecular image as due to the methyl groups. When the two isomers are coadsorbed, they exhibit complete mixing, and the individual components can be differentiated by their shape. At low coverage, both xylene molecules adsorb preferentially at the step edges, whereas on the terraces, they are mobile in the time scale of the STM imaging. Coadsorption with CO produces a mixed layer, and the xylene molecules become immobile.

Discrimination of double positioning by the nucleation of crystallites on molybdenite

Characteristic nucleation and coalescence features of indium (In) crystallites formed by vacuum deposition on fresh cleavage surfaces of molybdenite crystal (MoS 2) were observed and analyzed. Almost perfect nucleation discrimination of the so-called double positioning, which was reported by the authors very recently, was proved not to be affected appreciably by changes of deposition conditions: Depositions in a range of substrate temperatures from 25 to 85 °C, and at a rate from 0.8 to 10 Å/sec in a vacuum from 1 × 10 -4 to 5 × 10 -8 Torr gave almost the same discrimination ratios in the range 94 to 99%. The basal triangle of In crystallites having a distorted fcc structure is not equilateral but isosceles. The In crystallites were found to assume orientations which make the shortest side of the triangle parallel to one of the three equivalent 〈10 1 0〉 axes of MoS 2. The three orientations have angular misfit with each other on account of the tetragonal distortion. Coalescence among the crystallites of such orientations was found to proceed in a characteristic way, such that one of the coalescing crystallites keeps its original orientation throughout the coalescence event and the others rotate to make their one pyramidal plane parallel to a similar plane of the unrotated crystallite. An application of the almost perfect discriminating potency of an In deposit to the determination of the potency of other substances is suggested by showing a preliminary result for Au which gave values of 66% discrimination at 140 °C and 82% at 300 °C.

BIREFRINGENCE OF THE CORNEA

To the Editor: In reviewing the literature on corneal birefringence, I was intrigued by the observations of Cogan 1 on Haidinger's brushes, particularly the opposite rotation of the brushes when cellophane was interposed. Subsequent work on the phenomena by Stanworth and Naylor 2 provides beautiful corroboration of the dichroic macular theory of Helmholtz. 3 This theory explains the entoptic observation of Haidinger's brushes as the result of dichroic elements, having planes of polarization oriented with axial symmetry, within the macular region. Cogan's observations, too, fit this theory. A dichroic filter of this sort can be modeled readily using a Polaroid plane polarizing filter. The Polaroid filter itself consists of a multitude of uniformly oriented dichroic elements. The polarizer is cut into many narrow isosceles triangles or sectors, with the short base of each triangle parallel to the polarizing axis. These sectors are positioned side by side such that the sharp

V. Observations on the fundamental property of the lever; with a proof of the principle assumed by Archimedes, in his demonstration

V. Observations on the fundamental property of the lever; with a proof of the principle assumed by Archimedes, in his demonstration