I.D. Akçali

Selected Physical Properties of Peanuts

Selected physical properties of peanuts, which are effective in case of mobility or immobility were examined. For this aim, firstly, the geometrical shape of peanuts was defined and the specific mass and friction coefficient, which are quantitative measures of the inertia and frictional resistance that determine the ability of movement, were obtained. A geometrical shape consisting of a cylinder and two hemispheres at the ends has found quantitative appropriateness of at most 91% and at least 34% for the varieties in Turkish Standards. A variation of 0.37–0.58 g cm−3 for the solid density and that of 0.21–0.28 g cm−3 for the bulk density of hulled peanut have been found. The solid densities of kernel and shell have been determined in the range of 0.88–0.93 g cm−3 and 0.27–0.30 g cm−3, respectively. Their average bulk densities have been observed within 0.54–0.59 g cm−3 and 0.066–0.077 g cm−3 intervals, respectively. The angle of repose and internal friction angle measured by two methods have been in close agreement—around a 29° value. The friction coefficient has been found to be influenced by the materials in contact to a great extent, ranging from 0.23 for kernel on sheet metal up to 0.76 for hulled peanuts on an iron grate perpendicular to flow.

A Novel Approach in the Direct Kinematics of Stewart Platform Mechanisms with Planar Platforms

In handling the kinematic analysis of two rigid bodies connected to each other by six legs through the use of six double spherical joints, methods have been implemented both in the formulation and solution phases of the problem. A three-dimensional problem has been viewed, in fact, as a multitude of two-dimensional works on several planes, the intersections of which yield relationships allowing transition between adjacent planes. Thus formulation is purely based on the geometric structure consisting of eight planes of interest, ending in the three fundamental equations involving three angles between the base and side triangular planes. In solving the resulting three equations, an efficient strategy has been established to come up with 16 solution sets effectively. Extensions of the theory have been shown to include the analyses of other Stewart platform models. Efficiency and effectiveness of the approach has been verified on numerical examples.

Path generation by subdomain method

Abstract A technique called subdomain method has been used in dimensioning mechanisms which are to approximate a prescribed, continuous path. In this technique the motion domain is derived into subregions as many times as there are parameters existing within the kinematic structure and the system of equations, resulting from setting the integrals of a displacement function over selected subintervals equal to zero, is solved. Here a dyad is considered as the basic structural unit upon which the whole mechanism design is based. Solutions for 4-parameter dyad and for 4- and 5-parameter four-barfs have been shown. The effectiveness of the technique has been demonstrated on two examples.

Function generation by Galerkin's method

Abstract An original method referred to as Galerkins method in mathematics has been proposed for determining the dimensions of a mechanism which is to approximate a given continuous function. The application of this method has been shown on a four-bar for 3- and 5-parameter cases. Here synthesis has been realized by solving the system of equations derived from the conditions whereby the four-bar displacement function is orthogonal to a set of selected weighting functions, which are equal, in number, to the number of existing parameters and are continuous within domain interest. Its effectiveness has been demonstrated on several examples.

A Mathematical Model in the Implementation of a Stewart-Gough Platform as an External Fixator

In orthopedical practice, simple classical devices like rods, pins and hinges are widely used to deal with orthopedical disorders. However, these simple-looking tools complicate the pre-operative planning in removing such disorders as bone misalignments in connection with the extremity fracture and deformity cases. Thus, a novel approach is needed to take this burden off the orthopedist. In this work, a simplified procedure is proposed, in which a robotic frame is initially fixated easily at first to the fracture site and then fine-tuning in the alignment is done after processing medical input data within the framework of a mathematical model of the system. The robotic frame considered here is the so-called (6-6) type of Stewart-Gough Platform that consists of two platforms to which proximal and distal fragments are attached by means of six adjustable legs through the six spherical and six universal joints. Here, a mathematical model is developed to transform the medical input data obtained from antero-posterior (AP) and lateral (L) X-ray films and clinical examination into appropriate leg lengths required for the alignment process. To validate the mathematical model, the process is demonstrated on an example involving a specially designed and manufactured model of Stewart-Gough platform of (3-3) type as an external fixator and a physical model containing synthetic bone fragments.

A hybrid image processing system for X-ray images of an external fixator.

In the field of orthopaedics, treatment of extremity deformities can be realised by means of external fixators. However, control of such biomedical system is very difficult. Some different mathematical models have been developed to improve quality of this service. Most of the parameters, which are used in these models, have been obtained from two orthogonal X-ray images: one from anteroposterior, AP, direction and the other from a lateral, L, direction. The quality of the results of this model is dependent on the accuracy of the input parameters. Measuring these parameters is a time-consuming issue, and the accuracy of the results is also low. To increase the quality of the measurement, the reference points should be chosen from the edges of the biomedical system, and it is important to find the edges without noise. To achieve this purpose, Sobel edge detector, binary large object analysis, thresholding and inverting are applied as image processing steps. The results are compared with manual measurement values which have been obtained earlier. The results show that semi-automatic measurement of the parameters is more accurate and faster than manual measurement. It shows that the efficiency of the fixator method has been improved.

A theoretical and experimental investigation of lateral deformations in a unilateral external fixator

The objective of this work is to set up, validate, and analyze a theoretical model of an external fixator for its deformation characteristics in order to draw reliable conclusions relevant to the design and effective clinical implementation of such medical devices. External fixators are mechanical devices widely used in the treatment of fractured bones and correction of limb deformities. Lateral deformation at the fracture site is known to delay bone healing, and investigation of lateral deformation characteristics of such devices experiencing forces acting perpendicular to the bone axis is important from the standpoint of their design as well as their clinical effectiveness. A mathematical model of a three-dimensional (3D) unilateral fixator with multipin fragment attachments has been developed using Castigliano s method. The relative lateral deformations of the fragment ends at the fracture site induced by loads applied perpendicular to bone axes are calculated with the model. The model has been subjected to experimental verification for a uniplanar unilateral external fixator under comparable conditions with the theory. It has been found out that the effects of fixator size, shape, and geometry on the level of relative lateral displacement of the fracture site are similar in both the theoretical and experimental models. Stiffness is a maximum if the force is applied in the same plane as the proximal pin plane. Placing the distal pin group at a 90 deg position relative to the proximal pin plane has been observed to increase the stiffness about 10%. In loading directions perpendicular to proximal the pin plane, stiffness is minimum. The angle difference between the load direction and the resulting displacement-direction follows a sinusoidal pattern with an amplitude of 10 deg for loading angles in the 0-180 deg range. Selecting the distance of proximal pins to the fracture site smaller than the distance of distal pins to the fracture site has been found to decrease relative lateral deformation. The model and the experiment have simultaneously demonstrated that lower values of effective pin lengths and higher values of pin connector lengths lead to higher stiffness. Increasing the number of pins also contributes to the higher values of fixator stiffness.

Displacement Analysis of Robotic Frames for Reliable and Versatile Use as External Fixator

External fixators are widely used in the area of orthopedics to manage deformities and fractures. The historical trend in obtaining a mechanical infrastructure has shifted from simple devices like pins, rods, and hinges to more sophisticated frames involving parallel manipulators. Despite advantages of such robotic frames especially in removing stiffness issues, there are still problems associated with the reliable deployment of these modern devices. Problems like singularity, possibilities of guiding fragments along many different trajectories have been handled in this paper. A method has been shown how to detect singularity in displaced, aligned, and intermediate positions of the fragments. How the robotic system could be actuated according to different functions have been investigated, in addition to their effects on trajectories of distal fragment end. These considerations have been demonstrated on numerical examples.

Impact Resistance of Peanut

In this work, impact resistance of whole pod peanuts was studied, depending on its descriptive physical properties. An apparatus was designed and fabricated to realize this goal experimentally. In the experiment, a sufficient number of peanuts from each type supported on different materials underneath were struck by various materials in different configurations. The conditions of kernel and peanut shell were then recorded. The raw experimental data were processed by means of a developed computer program to evaluate the shelling percentage versus dynamic pressure, energy at impact, dynamic load, impact velocity, and dynamic deformation. Results showed that use of an iron grate in a shelling machine provided the most suitable material condition for the effectiveness of the impact method.

Development of constant output–input force ratio in slider–crank mechanisms

ABSTRACT In the slider–crank mechanism whereby output piston force is produced against an input force at crank pin centre, the output force varies rapidly when the crank changes its position. For the applications that require a constant piston pushing force as in feeder mechanisms, a method is needed for identifying the parameters to keep output force at a constant value for any crank angle position. Hence in this study, two methods are shown for a slider–crank mechanism operating in horizontal plane. In the first one, a manual control process to generate a constant piston force and the resulting errors are demonstrated. In the second one, identifying the parameters of a mechanical controller for a readily available slider–crank mechanism in an open force control process and the associated error state are shown. Then, an approach to optimize the results of open force control is explained. Finally, the developed methods are generalized for any orientation of the whole slider–crank mechanism. A user friendly interface is developed to transform all the processes into a computer programme. The effectiveness of the methods are numerically illustrated on examples. The results of these examples show that ±4% deviation from the required output force can be obtained pending on the user’s ability while the optimized open force control process provides a maximum error of ±0.4% without any user intervention during operation.