Abstract: In this paper, according to the classical algorithm
LSQR for solving the least-squares problem, an iterative method is
proposed for least-squares solution of constrained matrix equation. By
using the Kronecker product, the matrix-form LSQR is presented to
obtain the like-minimum norm and minimum norm solutions in a
constrained matrix set for the symmetric arrowhead matrices. Finally,
numerical examples are also given to investigate the performance.
Abstract: A new tool path planning method for 5-axis flank
milling of a globoidal indexing cam is developed in this paper. The
globoidal indexing cam is a practical transmission mechanism due
to its high transmission speed, accuracy and dynamic performance.
Machining the cam profile is a complex and precise task. The profile
surface of the globoidal cam is generated by the conjugate contact
motion of the roller. The generated complex profile surface is usually
machined by 5-axis point-milling method. The point-milling method
is time-consuming compared with flank milling. The tool path for
5-axis flank milling of globoidal cam is developed to improve the
cutting efficiency. The flank milling tool path is globally optimized
according to the minimum zone criterion, and high accuracy is
guaranteed. The computational example and cutting simulation finally
validate the developed method.
Abstract: Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.