In this paper we present a practical method for finding obstacle-free minimum-time motions for manipulators subject to the limits of velocity-dependent actuator forces. An optimal motion-planning problem is converted into a finite-dimensional nonlinear programming problem by means of parameter optimization with quintic B-splines. We introduce the concept of the minimum-overload trajectory in wh...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic Bsplines as weight functions has been developed to solve a general eighth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet, the N...

A finite element method involving collocation method with Quintic B-splines as basis functions has been developed to solve fifth order boundary value problems. The fifth order derivative for the dependent variable is approximated by the finite differences. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points se lected in ...

In our contribution we study cubic and quintic Pythagorean Hodograph (PH) curves in the Euclidean and Minkowski planes. We analyze their control polygons and give necessary and sufficient conditions for cubic and quintic curves to be PH. In the case of Euclidean cubics the conditions are known and we provide a new proof. For the case of Minkowski cubics we formulate and prove a new simple geome...

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and respectively produce sequences of vertices fk and bk. The Js refinement proposed here produces vertices vk=(1–s)fk+sbk. Iterative applications of Js yield a family of curves parameterized by s. It includes the four-point curve (J0), the un...

Cycle time minimization is one of the major goals to achieve in manufacturing. Maximizing feedrate direct solution; however, physical motions need be under specified motion limits avoid high-frequency vibration, causing machining error. In this paper, a time-optimal scheduling approach with corner smoothing for 5-axis G1 toolpaths presented machining. One key feature proposed method describe or...

‎In this paper we introduce a numerical approach that solves optimal control problems (OCPs) ‎using collocation methods‎. ‎This approach is based upon B-spline functions‎. ‎The derivative matrices between any two families of B-spline functions are utilized to‎ ‎reduce the solution of OCPs to the solution of nonlinear optimization problems‎. ‎Numerical experiments confirm our heoretical findings‎.

Surface offset is one of the most useful operations in Computer Aided Geometric Design (CAGD). However, an implementation of this operator is not trivial primarily because the offset surface, in general, does not have the same representation as the original surface. Hence, it is dif®cult or impossible to represent an exact offset in a system with limited surface forms. For this reason, some CAG...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions has been developed to solve a general seventh order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and ...

Conventional tool paths for computer numericalcontrolled (CNC) machine tools or NC positioning systems are mainly composed of linear motion segments, or the socalled G1 commands. This approach exhibits serious limitations in terms of achieving the desired part of geometry and productivity in high-speed machining. Velocity and acceleration discontinuities occur at the junction points of consecut...