Mirjana Filipovic

Expansion of source equation of elastic line

The paper is concerned with the relationship between the equation of elastic line motion, the “Euler-Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

Complement of Source Equation of Elastic Line

A new notion of joint, defined in terms of the state of motor (active or locked) and type of the elastic or rigid element, gear and/or link that follows after the motor, is introduced. Special attention is paid to the motion of the flexible links in the robotic configuration. The paper deals with the relationship between the equation of elastic line equilibrium, the “Euler–Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the elasticity moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and cannot be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. The choice of reference trajectory is analyzed. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the gear and of the link (two modes), as well as the environment force dynamics.

Relation between euler-bernoulli equation and contemporary knowledge in robotics

The motivation for this work is the state of modern structural mechanisms that are characterized by growing complexity and ever-increasing demands for rapid and accurate motion. These contradictory requirements are often achieved according to easier and easier structures characterized by flexibility segments. In most of cases, the elasticity of structures appears as an obstacle for a precise and rapid control of motion. The aim of this paper is to explore ways of implementation of structural properties of elasticity with the application of high fidelity models during synthesis and analysis of complex mechanisms. Precisely, the aim is to explore the possibility of using Euler-Bernoulli equation, if not in its original form, then to the same extent with the use of modern knowledge in robotics (based on the knowledge of classical mechanics), and to examine the affordability and confirmation of the method through simulation results for a typical robotic configuration.

Correlation of microstructure with the wear resistance and fracture toughness of white cast iron alloys

The objective of this investigation was to set down (on the basis of the results obtained by the examination of white cast iron alloys with different contents of alloying elements) a correlation between chemical composition and microstructure, on one hand, and the properties relevant for this group of materials, i.e., wear resistance and fracture toughness, on the other. Experimental results indicate that the volume fraction of the eutectic carbide phase (M3C or M7C3) have an important influence on the wear resistance of white iron alloys under low-stress abrasion conditions. Besides, the martensitic or martensite-austenitic matrix microstructure more adequately reinforced the eutectic carbides, minimizing cracking and removal during wear, than did the austenitic matrix. The secondary carbides which precipitate in the matrix regions of high chromium iron also influence the abrasion behaviour. The results of fracture toughness tests show that the dynamic fracture toughness in white irons is determined mainly by the properties of the matrix. The high chromium iron containing 1.19 wt% V in the as-cast condition, showed the greater fracture toughness when compared to other experimental alloys. The higher toughness was attributed to strengthening during fracture, since very fine secondary carbide particles were present mainly in an austenitic matrix.

Sintered Materials Based on Copper and Alumina Powders Synthesized by a Novel Method

The intensification in research of nanostructure materials that occurred in recent years was mainly due to their striking potential, i.e. mechanical and physical properties significantly improved compared to the conventional grain materials (Moriarty, 2001; Ristić, 2003). Nano-structured materials rank in the group of ultra fine, metastable structures containing a high concentration of defects (point defects, dislocations) and boundaries (grain boundaries, interphase boundaries, etc.). These materials are structurally different from crystals and amorphous forms because of the fact that grain boundaries and interphases represent a specific state of the solid matter, since the atoms on boundaries are subjected to a periodical potential field of the crystal from both sides of the boundary (Koch, 1999). The synthesis of powders represents the starting and crucial stage in the production of sintered metal materials with required properties. Considering that the starting structure undergoes certain changes during further processing, but remains essentially preserved in the structure of the final product (Ristić, 2003; Motta et al. 2004), there is an increased necessity for a great number of methods for producing powders. Copper is widely exploited in industry because of its high electrical and thermal conductivity, even though it possesses low strength especially at elevated temperatures. In order to overcome this problem it can be strengthened by using finely dispersed particles of stable oxides like alumina, titania, yttria etc. Copper-based composite materials are widely applied in the field of electronics and electrical engineering as highly conductive materials for operation at elevated temperatures, as electrodes for resistance spot and seam welding, different contact materials, various switches, thermal and electric conductors, microwave tubes, etc (Lee & Kim, 2004). Introduction of fine dispersed particles into matrix of base-metal has considerable strengthening effect and nano particles of oxides are especially suitable. Due to their hardness, stability at elevated temperatures and insolubility in copper they represent obstacles for dislocation, grain and sub-grain boundary movement increasing mechanical properties of these materials with insignificant effect on thermal and electrical conductivity (Naser et al., 1997; Trojanova et al., 1999, Tian et al. 2006). Significant reinforcing effects can

Dynamic accuracy of robotic mechanisms. Part 1: Parametric sensitivity analysis

Abstract The paper is organized in two parts. Part 1 treats the problem of robot dynamic accuracy which has been scarcely elaborated in the literature. In this paper the error model of control by means of local feedback loops is given, which represents the initial research results in that field (N. Vesovic, M. Vukobratovic, Mech. Mach. Theory 29 (1994) 415–425). In this paper the error model of tracking trajectories using a dynamic control law, was developed and presented in detail. By using the inverse dynamics method (IDM) a control law was formed, into which the robot dynamics model was included and the sensitivity functions, which have served as the basis for the analysis of the variations influence on the dynamic robot parameters of the trajectory tracking accuracy were given.

Dynamic accuracy of robotic mechanisms. Part 2 : Simulation experiments and results discussion

Abstract In Part 1 of this paper the theoretical fundamentals of the robotic mechanisms accuracy using various dynamic control laws were considered. Based on the error model and the adopted control laws, a basis was formed for extensive simulation experiments. In this part of the paper, the simulation conditions were chosen and the criterion was adopted for the analysis and comparison of the sensitivity functions. Conclusions were made based on the previously denned criteria and by that the analysis of the dynamic parameters influence on the trajectory tracking accuracy was carried out.

Graphical representation of the significant 6R KUKA robots spaces

Trajectory planning for serial 6 degree of freedom (DOF) machinery systems is demanding due to complex kinematic structure which affects the machinery tool fame, position, orientation and singularity. These three characteristics represent the key elements for production planning and layout design of the manufacturing systems. Both, simple and complex machine trajectory is defined as series of connected points in 3D space. Each point is defined with its position and orientation related to the machines base frames. To visualize the machines reachable space, the work envelope is calculated and graphically presented as very well known machines property. A methodology to predetermine regions of feasible tool orientation (work window) is analytically and graphically presented. The work envelope boundary is generated using the filtering points algorithm, while work window is generated using either empirical or analytical methods. The singularity regions are calculated by finding the determinant of the reconfigurable Jacobian matrix. These three tool path characteristics represent three different spaces which are identified both analytically and graphically and plotted in Cartesian space using MATLAB tools. The singularity regions will be represented within the workspace and work window for a single machinery kinematic structure. The KUKA KR robot family is used as a case study.

Contribution to the modeling of cable-suspended parallel robot hanged on the four points

This paper describes a novel mathematical model of the Cable-suspended Parallel Robot. The complex system is made to accurately carry camera in the 3D space. The geometric relationship between the camera motion in the Cartesian coordinates and motors angular positions is defined by the Jacobian matrix, which represents the solution of the kinematic problem. The solution of the calculated matrix directly depends on the systems geometry. The adopted Jacobian matrix is used for calculation of the dynamic model of the Cable-suspended Parallel Robot. Two numerical examples are used to illustrate practical usefulness of the proposed mathematical model and its validation. The final goal of this research is to ensure the accurate and highly automated guidance of the camera in 3D space with the minimal involvement of the human factor for the task generation.

Euler-Bernoulli equation today

Special attention is paid to the motion of the flexible links in the robotic configuration. The elastic deformation is a dynamic value which depends on the total dynamics of the robot system movements. The Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the elasticity moment of the considered mode according to the requirements of the motion complexity of elastic robotic systems. This yields the difference in the structure of Euler-Bernoulli equations for each mode. The stiffness matrix is a full matrix as well as damping matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral which defined Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the mechanism elastic line is a direct outcome of the system motion dynamics, and cannot be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the gear and of the link (two modes), as well as the environment force dynamics.