The Issue of Calculating Elliptic Trajectories

Abstract

The design of elliptic trajectories of kinematic mechanisms by classical method is a challenge. New method is proposed. Theoretical tests were conducted on a method. It can not be used for scaling and rotation. Some limitations are revealed as well. Geometric modeling showed the method can be applied to arbitrary curves. It should be noted that the theoretical and modeling researches of arbitary curves is not full. Simple robot was designed for processing ellipses. The design of the stand was assembled from aluminum profiles, linear modules and fasteners RK Rose + Krieger. Experiments have shown a difference between the theoretical and actual trajectory less than 5%. The error of stationing was 8,5% before using of the direct analytical method.

The precision calculating method of robots moving by the plane trajectories

“…18,19 Further theoretical and experimental studies made it possible to substantiate the applicability of this method to Jordan curves. 20 The new method was tested in computer geometric modeling and on the trajectories of robot tests in laboratory conditions. Recent studies have made it possible to find a general calculation algorithm on a nonorthogonal basis.…”

Machine Vision System Measuring the Trajectory of Upper Limb Motion Applying the Matlab Software

“…In module "Input data entering", a photograph which will further be processes being loaded, and also all variables of the program, are initiated: the measure of the elbow angle, the measured value of the angle between the arm and the chest, the table recorded localizations of markers, etc. [24]- [27].…”

A new novel six-degree of freedom two-link manipulator using active magnetic bearing: Design, kinematics, and control

“…The BLDC motor parameters are given in Table 7 for joint 2 and Table 8 for joint 1. The system and its controllers represented by equations (14) to (50) are all simulated using MATLAB/Simulink. 28 In order to control the end effector position and orientation of the proposed two-link manipulator to be, for example, at (x e , y e , z e ) ¼ (À250 mm, 100 mm, À150 mm) and ( e , q e , e ) ¼ (30 , À125 , À225 ), considering macro positioning of the joint roll angle, e ¼ 30 , equation (34) and equation (37) to equation (48) are used to obtain the required robot joint roll angles ( 2 ) and the air gap deviations of the radial and axial motions (g 0 l1 2 , g 0 r1 2 , g 0 l3 2 , g 0 r3 2 , g 0 la 2 ) of joint 2 as well as ( 1 ) and (g 0 l1 1 , g 0 r1 1 , g 0 l3 1 , g 0 r3 1 , g 0 la 1 ) of joint 1.…”

“…However, the polishing head of the end effector is driven by geared AC motor and the bearing is of contact type. Other studies of controlling robot arm movement in one-axis direction and mobile robot arm position control are investigated in the study by Božek et al, 12 Turygin et al 13 , and Lozhkin et al 14 In a previous work, a 6-DOF robotic joint with AMB was designed in the study by Selmy et al 7 Despite the good performance of that joint, it suffers from limited workspace of the end effector movement. Thus, to overcome these limitations, a new two-link manipulator with two novel contactless 6-DOF joints is proposed and developed in this article.…”