Development of Alternative Methods for Robot Kinematics

The problem of finding mathematical tools to represent rigid body motions in space has long been on the agenda of physicists and mathematicians and is considered to be a well-researched and well-understood problem. Robotics, computer vision, graphics, and other engineering disciplines require concise and efficient means of representing and applying generalized coordinate transformations in three dimensions. Robotics requires systematic ways to represent the relative position or orientation of a manipulator rigid links and objects. However, with the advent of high-speed computers and their application to the generation of animated graphical images and control of robot manipulators, new interest arose in identifying compact and computationally efficient representations of spatial transformations. The traditional methods for representing forward kinematics of manipulators have been the homogeneous matrix in line with the D-H algorithm. In robotics, this matrix is used to describe one coordinate system with respect to another one. However for online operation and manipulation of the robotic manipulator in a flexible manner the computational time plays an important role. Although this method is used extensively in kinematic analysis but it is relatively neglected in practical robotic systems due to some complications in dealing with the problem of orientation representation. On the other hand, such matrices are highly redundant to represent six independent degrees of freedom. This redundancy can introduce numerical problems in calculations, wastes storage, and often increases the computational cost of algorithms. Keeping these drawbacks in mind, alternative methods are being sought by various researchers for representing the same and reducing the computational time to make the system fast responsive in a flexible environment. Researchers in robot kinematics tried alternative methods in order to represent rigid body transformations based on concepts introduced by mathematicians and physicists such as Euler angle or Epsilon algebra. In the present work alternative representations, using quaternion algebra and lie algebra are proposed, tried and compared

Structural characterization and modelling of fly ash brick masonry

The disposal of fly ash is an environmental challenge globally, and the only viable solution for its mass disposal is its use in the construction industry, especially for brick production. Hence, recent times saw substantial growth in masonry structures using fly ash bricks in India, where coal-based power plants dominate the power sector. However, the performance of a masonry structure is dependent upon the properties of the bricks along with several other factors. Hence, the evaluation of fly ash brick properties is essential for quality masonry construction. The present research is an effort to study the engineering properties of fly ash brick unit and masonry on a large scale, establish the correlation among these properties, and quantify variability associated with different strength properties. Basic engineering properties like water absorption, initial rate of absorption, dry density, and compressive strength is studied on a large no of brick specimens, and the obtained result is checked for its suitability in quality construction. Among all the parameters, brick compressive strength is the key property that strongly influences the masonry compressive strength. Hence, the proper information regarding the brick compressive strength is essential before using it in masonry work. However, the evaluation of compressive strength requires access to sophisticated instruments, which is generally not available in the majority of the construction sites. This calls for the development of an alternative method that could provide first-hand knowledge on the strength and quality of brick units without the need for any large testing equipment. For this purpose, the correlation between the compressive strength and other easily measurable parameters is studied and a mathematical model is developed to predict the fly ash brick compressive strength using other parameters through experimental results and statistical correlation. An empirical model is also proposed to predict the compressive strength of fly ash brick masonry assemblages. The proposed models are validated using the experimental results reported in the previous literature. These models can be used as a quality control tool for fly ash bricks and masonry at the construction site. Moisture content or saturation level of the brick unit at the time of construction is another key factor contributing to the bond strength of masonry. Masonry wall resists both in-plane and out-of-plane forces through the bond between the brick unit and mortar. Absorption of water from mortar by brick alters the development of a mechanical key that establishes the bond strength. The effect of moisture content of bricks, at the time of construction, on shear and tensile bond strength of fly ash brick masonry is investigated. The results of this study indicate that around 75% saturation level of the brick unit yields the highest values of shear and tensile bond strength of fly ash brick masonry with cement mortar. Adequate pre-wetting of brick units at the time of construction will ensure the desired moisture content and, subsequently, help to achieve a good bond strength. The strength properties of fly ash brick masonry can show a significant variation because of several influencing factors like source and proportion of constituent materials, workmanship, curing condition among others. Quantification of this uncertainty is essential for the reliability-based limit state design of masonry structures. Safety and strength assessment of structures made of fly ash bricks often require modelling the uncertainty of its properties. The present study investigates the variability associated with compressive strength, shear-, split tensile-, and flexure tensile-bond strength of fly ash brick masonry and proposes the most appropriate model for its statistical distribution. Ten probability distributions are considered to conduct the three goodness of fit tests, namely Kolmogorov-Smirnov, Kolmogorov-Smirnov-Lilliefors, and Anderson-Darling tests. The analysis shows that conventionally assumed normal distribution is not suitable for describing the strength properties of fly ash brick masonry as the experimentally obtained strength data is not symmetrical about its mean value. The best-fitted distribution functions that perform well in describing the variability in different strength properties of fly ash brick masonry are recommended. A case study on the seismic risk of a typical reinforced concrete framed building infilled with fly ash masonry is performed considering different probability distribution functions. The results of the case study indicate that the choice of the probability distribution of the random variables influences the seismic risk assessment of structures significantly and consideration of the appropriate distribution function is vital for the precise estimation of seismic ris