The simulation of robot systems is becoming very popular, especially with the lowering of the cost of computers, and it can be used for layout evaluation, feasibility studies, presentations with animation and offline programming.The trajectory planning of redundant manipulators is a very active area since many tasks require special characteristics to be satisfied. The importance of redundant manipulators has increased over the last two decades because of the possibility of avoiding singularities as well as obstacles within the course of motion. The angle that the last link of a 2 DOF manipulator makes with the x-axis is required in order to find the solution for the inverse kinematics problem. This angle could be optimized with respect to a given specified key factor (time, velocity, torques) while the end-effector performs a chosen trajectory (i.e., avoiding an obstacle) in the task space.Modeling and simulation of robots could be achieved using either of the following models: the geometrical model (positions, postures), the kinematic model and the dynamic model.To do so, the modelization of a 2-R robot type is implemented. Our main tasks are comparing two robot postures with the same trajectory (path) and for the same length of time, and establishing a computing code to obtain the kinematic and dynamic parameters.SolidWorks and MATLAB/Simulink softwares are used to check the theory and the robot motion simulation.This could be easily generalized to a 3-R robot and possibly therefore to any serial robot (Scara, Puma, etc.).The verification of the obtained results by both softwares allows us to qualitatively evaluate and underline the validityof the chosen model and obtain the right conclusions. The results of the simulations are discussed and an agreement between the two softwares is certainly obtained.

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Kinematics analysis studies the relative motions, such as, first of all, the displacement in space of the end effector of a given robot, and thus its velocity and acceleration, associated with the links of the given robot that is usually designed so that it can position its end-effector with a three degree-of-freedom of translation and three degree-of-freedom of orientation within its workspace. This chapter presents mainly, on the light of both main concepts; the first being the screw motion or/ and dual quaternions kinematics while the second concerns the classical 'Denavit and Hartenberg parameters method' the direct kinematics of a planar manipulator. First of all, examples of basic solid movements such as rotations, translations, their combinations and general screw motions are studied using both (4x4) matrices rigid body transformations and dual quaternions so that the reader could compare and note the similarity of the results obtained using one or the other method. Both dual quaternions technique as well as its counterpart the classical 'Denavit and Hartenberg parameters method' are finally applied to a three degree of freedom (RRR) planar manipulator. Finally, we and the reader, can observe that the two methods confirm exactly one another by giving us the same results for each of the examples and applications considered, while noting that the fastest, simplest more straightforward and easiest to apply method, is undoubtedly the one using dual quaternions. As a result this work may as well act as a beginners guide to the practicality of using dual-quaternions to represent the rotations and translations ie: or any rigid motion in character-based hierarchies. We must emphasize the fact that the use of Matlab software and quaternions and / or dual quaternions in the processing of 3D rotations and/or screw movements is and will always be the most efficient, fast and accurate first choice. Dual quaternion direct kinematics method could be generalised, in the future, to more complicated spatial and/ or industrial robots as well as to articulated and multibody systems.

Various researchers have developed a model of conventional H2O -LiBr absorption machines, with the aim of predicting their performance. In this paper, the methodology of the adaptation of the characteristic equations is applied; this model is able to represent the cooling capacity of the double effect absorption chiller by means of simple algebraic linear equation. As a result, it is concluded that a good agreement between the theoretical simulation using the thermodynamic model and the results obtained on the literature. The results achieved through the adapted characteristic equations model have a deviation less than 10% for the cooling capacity and the coefficient of performance COP, and less than 15% for the heat capacity comparing to the thermodynamic model results. The developed characteristic equations and their assessment are useful for the simulation and the control purpose.