Natural Frequencies of a Manipulator with Rigid Tip Mass: the Case of Flexural-Flexuraltorsional Coupling

The characteristic (or frequency) equation of a flexible manipulator with a rigid tip mass is derived. The manipulator is modelled as an Euler-Bemoulli beam and it permits flexural (bending) deformation in two planes and torsional deformation. The position of the centroid of the tip mass may not necessarily be coincident with the elastic axis of the beam. This is represented by the use of offset coordinates. The natural frequencies of the manipulator are obtained by solving the characteristic equation. The results are compared to the results in the literature, where possible, and also to those obtained using a commercial finite element software ANSYS. The effects of the magnitude of the tip load, offset of the tip mass centre of gravity from its point of attachment, the length of the beam and slenderness ratio on the natural frequencies are examined.

Natural Frequencies of a Manipulator with Rigid Tip Mass: the Case of Flexural-Flexuraltorsional Coupling

The characteristic (or frequency) equation of a flexible manipulator with a rigid tip mass is derived. The manipulator is modelled as an Euler-Bemoulli beam and it permits flexural (bending) deformation in two planes and torsional deformation. The position of the centroid of the tip mass may not necessarily be coincident with the elastic axis of the beam. This is represented by the use of offset coordinates. The natural frequencies of the manipulator are obtained by solving the characteristic equation. The results are compared to the results in the literature, where possible, and also to those obtained using a commercial finite element software ANSYS. The effects of the magnitude of the tip load, offset of the tip mass centre of gravity from its point of attachment, the length of the beam and slenderness ratio on the natural frequencies are examined.

Prediction of angle error due to torsional deformation in non-circular grinding

Non-circular grinding is used in the grinding of crankshafts. In contrast to general grinding, the precision in non-circular grinding is affected by torsional deformation, which results in errors in the grinding depth. In this study, an equation to detect the angle error caused by torsional deformation is established considering the grinding force, the structure of the crankshaft, and the distribution of torque. The angle error due to torsional deformation was found to be up to 0.44 arcsec, which is 5 % of the angle error obtained from previous studies. This difference occurred as the previous studies did not exclusively detect the errors caused by bending deformation and torsional deformation. However, the established equation detects these errors separately. The fundamental cause of the two errors is the change in the structure of the crankshaft caused by bending. Further, the errors were eliminated via steady rest to reduce the bending of the crankshaft. Although the proposed equation is not entirely error-free, the results obtained by the equation have higher accuracy than those of previous studies.