Analytical graphic statics

Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived, little emphasis has been placed on studying the mathematics behind these methods. Due to the considerable advances of our mathematical understanding since the birth of graphic statics, we can learn a lot by examining these old methods from a more modern viewpoint. As such, this work shows the mathematical fabric joining different aspects of graphic statics, like dualities, reciprocal diagrams, and discontinuous stress functions. This is done by introducing a new, three dimensional force diagram (containing the old two dimensional force diagram) depicting the three dimensional equilibrium of planar force systems. A corresponding three dimensional “form diagram” (dual diagram) is introduced, in which forces are treated as linear functionals (dual vectors). It is shown that the polyhedral stress function introduced by Maxwell is in fact a linear combination of these functionals; and the projective dualities connecting these three dimensional diagrams are also explained.

Diagnosing Soft Tissue Sub-Surface Masses Using the XCS Classification System

Introduction: One of the most common types of cancer is breast cancer, which is considered as the second leading cause of death in women in Iran. Due to the fatality of this type of cancer, it is very important to diagnose the disease in the early stages and starting the treatment process. One of the methods to diagnose breast cancer is using mechanical arms (robot manipulator) to touch and measure the force in terms of displacement at the site of the breast touch by the robot. The hardness of the cancer tissue can affect the force diagram in terms of displacement, which can be used as a diagnostic method. The present study was performed to prepare a simulation model of breast soft tissue behavior considering subsurface masses. Then, a proposed classification system was designed to fit it.Material and Methods: In this section, first, the soft tissue behavior of the breast is simulated by considering sub-surface masses. The simulations are performed for a piece of tissue that is in the shape of a rectangular cube, as well as different dimensions of a spherical mass that is located at different depths and coordinates. Using simulation, various force-displacement diagrams have been obtained, based on which a data network.Results: The displacement force diagram for different modes is obtained using simulation. By giving the resulting diagrams to the trained system, the size and depth of the mass is determined. By comparing the obtained results with the initial model and the actual size and depth of the mass, a very good conformity is observed, which indicates the correct operation of the designed system and the performed simulation process.Conclusion: The proposed design system was used to diagnose the presence of tumors in tissue with sub-surface mass. The results show a high percentage of this method in diagnosis. However, the accuracy of this method can be greatly increased by increasing the amount of data given to the XCS system for training. On the other hand, instead of simulation data, test data on healthy and unhealthy people can be used for training.

Graphic kinematics, visual virtual work and elastographics

In this paper, recent progress in graphic statics is combined with Williot displacement diagrams to create a graphical description of both statics and kinematics for two- and three-dimensional pin-jointed trusses. We begin with reciprocal form and force diagrams. The force diagram is dissected into its component cells which are then translated relative to each other. This defines a displacement diagram which is topologically equivalent to the form diagram (the structure). The various contributions to the overall Virtual Work appear as parallelograms (for two-dimensional trusses) or parallelopipeds (for three-dimensional trusses) that separate the force and the displacement pieces. Structural mechanisms can be identified by translating the force cells such that their shared faces slide across each other without separating. Elastic solutions can be obtained by choosing parallelograms or parallelopipeds of the appropriate aspect ratio. Finally, a new type of ‘elastographic’ diagram—termed a deformed Maxwell–Williot diagram (two-dimensional) or a deformed Rankine–Williot diagram (three-dimensional)—is presented which combines the deflected structure with the forces carried by its members.

To Solve the Load of Beam by Shearing Force Diagram and Bending Moment Diagram - Reverse Thinking in Strength of Materials

The paper has a discussion of forward problem and inverse problem for beams in strength of materials. Known load case of a beam can certainly determine its shearing force diagram and bending moment diagram, but conversely, there may be a variety of statically determinate or statically indeterminate constraint conditions. Furthermore, the solution from statically indeterminate constraint conditions doesnt agree with the given shearing force diagram and bending moment diagram in a general way.

Mechanical Analysis of Snake-Like Robot for Colonoscopy

In order to develop a robot for colonoscopy, which can provide the same functions as conventional colonoscope, but much less pain and discomfort for patient, a snake-like robot with continuum structure is proposed. The mechanical structure of snake-like robot for colonoscopy is introduced and the angle of single section is calculated. The mechanical model of cantilever beam is built, the force diagram is drawn and the mechanical analysis of single section in bending process is mainly analyzed. Finally, ‘Pro/E’ is used to build model and simulate the process that the snake-like body goes through the colon. This paper lays foundation for the research on snake-like robot for colonoscopy.

A diagram of the minimum necessary internal force required to resist external forces on two-point-grasped objects in two-dimensional space

SUMMARYThis paper considers the magnitude of the gripping power, i.e., the internal force that depends on the grasping posture or object orientation in a two-dimensional grasp by two contact points with friction. Expressing the effect of variations in the object posture as the direction of an external force, we propose an “internal force diagram.” The internal force necessary to create a statically stable grasp is depicted in the object coordinate frame. Then, a polar coordinate system is introduced in which the orientation represents the direction of the external force, while the distance from the origin represents the minimum necessary internal force. We demonstrate a method based on friction cone configurations to manually draw the internal force diagram, using only a ruler and a compass. The validity of this drawing method is confirmed by a comparison with computer-generated plots. Finally, the characteristics of the internal force diagram are discussed.