The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...

A new control method for kinematically redundant manipulators having the properties of local torqueoptimality and singularity-robustness is developed. The proposed control method is applied to the numerical model of the SNU-ERC 3-DOF direct-drive manipulator. It is shown that the proposed control method is very e ective in overcoming the singularity problem, especially in the case of using the ...

We discuss the singularity in the Borel plane of the ultraviolet renormalon due to the multiple exchanges of the all-order Gell-Man–Low effective charges. A consistent picture of the UV renormalon emerges when the effective charge is considered in all orders. Contrary to the case of the one-loop effective charge, the strength of the singularity is independent of the number of exchanges. A syste...

In this paper, an algorithm is proposed to avoid singularity associated with the most famous minimum element attitude parametrization, Euler angle set. The proposed algorithm makes use of the method of sequential rotation to avoid singularity associated with Euler angle set. Further, a switching algorithm is also proposed to switch between different Euler angle sets to avoid the singularity whi...

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is widely used in rigid-body shape changing mechanisms. The general singularity equation is reduced to a condensed form, which allows geometric relationships to be readily detected. A method for formulating the singularity condition for...

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch singularity of a real algebraic surface. For such singularities, the va...

This paper addresses the problem of identifying the property of the singularity loci of a class of 3/6‐ Gough‐Stewart manipulators for general orientations in which the moving platform is an equilateral triangle and the base is a semiregular hexagon. After constructing the Jacobian matrix of this class of 3/6‐Gough‐Stewart manipulators according to the screw theory, a...

The present paper investigates an intuitive way of robot path planning, called robot teaching by demonstration. In this method, an operator holds the robot end-effector and moves it through a number of positions and orientations in order to teach it a desired task. The presented control architecture applies impedance control in such a way that the end-effector follows the operator’s hand with d...

This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The algorithm is based on Grassmann-Cayley algebra. The proposed tool is interactive and introduces the designer to the singularity analysis performed by this method, showing all the stages along the procedure and eventually showing the solution algebraically and graphically, allowing as we...