The hexagonal grid has long been known to be superior to the more traditional rectangular grid system in many aspects in image processing and machine vision related fields. However, systematic developments of the mathematical backgrounds for the hexagonal grid are conspicuously lacking. The purpose of this paper is to study geometric transformations on the hexagonal grid. Formulations of the transformation matrices are carried out in a symmetrical hexagonal coordinate frame. A trio of new trigonometric functions are defined in this paper to facilitate the rotation transformations. A fast algorithm for rounding an arbitrary point to the nearest hexagonal grid point is also presented.
In this paper we present an analytical scheme for the displacement analysis of micropositioning stages with flexure hinges. The proposed scheme is based on linearization of the geometric constraint equations of the stage structure. A design chart for evaluating the stiffness of the flexure hinge is also presented in this paper. This chart provides more accurate estimations than the design formula presently in use. The proposed linear scheme is general, easy to use, yet capable of obtaining results close to those obtained from the finite element analysis.
While much has been contributed to techniques for enumerating and identifying rigid-body mechanisms in the past decades, proportionally little has been accomplished in this regard in compliant mechanisms design. This paper deals primarily with identification and discussion of important kinematic properties of compliant mechanisms. To facilitate these appropriate terminology is developed at the very fundamental level. The conventional degrees-of-freedom concept for a rigid-body chain is briefly reviewed. It is then used to help define a compliance number (or degrees-of-compliance) concept for characterizing compliant mechanisms. Finally, a systematic and convenient approach is presented, enabling the type synthesis of this class of mechanisms.
In modern day, from planetary exploration, disaster response to antiterrorism mission multiped robot has become the major tool. Smart robot with effective gait plan may play a significant role in such missions. But if a leg is injured, it is not possible to repair in this kind of mission. Then robot needs some alternative strategies to complete its mission. This paper proposes a removable sliding leg approach to solve this problem. A fault leg can be detaches and other legs can be slide to better position by the command of operator to get optimum alternative gait configuration. Based on leg sequence, stride length, longitudinal stability and efficiency, alternative gaits are evaluated. This paper recommends tables for different gait sequence with progressive efficiency. These tables can provide options for alternative gait and information about certain damaged leg. Moreover, a procedure for a multi-legged robot to complete its mission after serious leg failure is included. By taking the recommended tables and procedure, the multiped Robot can overcome any fault event and maintain stability and efficiency.
This paper investigates the hexagonal tessellation of picture elements used in computer graphics and computer vision systems. Its purpose is to propose a symmetrical hexagonal coordinate frame to replace the existing oblique coordinate system. In the proposed symmetrical coordinate frame, spatial properties of the hexagonal grid such as distance functions are better represented.
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