Kinematic analysis of spatial mechanical systems using exponential rotation matrices

The mathematical properties associated with the exponential rotation matrices are reviewed. By means of two typical mechanism examples, it is demonstrated that these properties constitute a versatile analytical tool, which can be used eftectively in kinematic studies on spatial mechanical systems involving position, velocity, acceleration, and singularity analyses.


A method of inverse kinematics solution including singular and multiple configurations for a class of robotic manipulators
Balkan, Raif Tuna; Özgören, Mustafa Kemal; Arıkan, Mehmet Ali Sahir (2000-09-01)
A semi-analytical method and an associated computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in the wrist point equations. For this case, it becomes possible to express all the other joint variables in terms of a selected one. and this reduces the inverse kinematics problem to solving a non-linear scalar equation having the selected joint variable as the only unknown. The solution can be obtained by iterative method...
A Density Functional Study of Ni-2 and Ni-13 Nanoclusters
Önal, Işık; Uzun, Alper; ÖZKAR, SAİM (2009-04-01)
Ni-2 and Ni-13 clusters have been studied by means of DFT calculations performed at B3LYP level using three different basis sets. Equilibrium geometry calculations resulted in a binding energy of nickel dimer of 1.078 eV/atom for the basis set m6-31G*, showing good agreement with experimental data. Ni-13 nanocluster was found to have an equilibrium structure of icosahedral for all three basis sets in accordance with experimental findings. The intercept of the line obtained by drawing a correlation line of b...
Kinematic and Kinetostatic Analysis of Parallel Manipulators with Emphasis on Position, Motion, and Actuation Singularities
Özgören, Mustafa Kemal (2019-04-01)
This paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are enco...
Kinematic analysis of a manipulator with its position and velocity related singular configurations
Özgören, Mustafa Kemal (1999-10-01)
Forward and inverse kinematic analyses of a generic 6-R serial manipulator are carried out at both position and velocity levels. Singular configurations associated with the inverse position solution, designated as position related singular configurations (POSCs), and those associated with the inverse velocity solution, designated as velocity related singular configurations (VESOs), are investigated. At POSCs, the specified pose of the hand is not sufficient to determine some of the joint variables; the moti...
Density functional theory investigation of two-dimensional dipolar fermions in a harmonic trap
Toffoli, Hande; TANATAR, BİLAL (2014-08-13)
We investigate the behavior of polarized dipolar fermions in a two-dimensional harmonic trap in the framework of the density functional theory (DFT) formalism using the local density approximation. We treat only a few particles interacting moderately. Important results were deduced concerning key characteristics of the system such as total energy and particle density. Our results indicate that, at variance with Coulombic systems, the exchangecorrelation component was found to provide a large contribution to...
Citation Formats
M. K. Özgören, “Kinematic analysis of spatial mechanical systems using exponential rotation matrices,” JOURNAL OF MECHANICAL DESIGN, pp. 1144–1152, 2007, Accessed: 00, 2020. [Online]. Available: