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Purpose -The aim of this paper is to develop a redundancy-resolution (RR) algorithm to optimize the joint space trajectory of the six-rotation-axis industrial robot as performing arc-welding tasks. Design/methodology/approach -The rotation of the tool around its symmetry axis is clearly irrelevant to the view of the task to be accomplished besides some exceptional situations. When performed with a general 6-degrees-of-freedom (DOF) manipulator, there exists one DOF of redundancy that remains. By taking advantage of the symmetry axis of the welding electrode, the authors decompose the required instantaneous twist of the electrode into two orthogonal components, one lying into the relevant task subspace and one into the redundant task subspace, respectively. Joint-limits and singularity avoidance are considered as the optimization objectives. Findings -The twist-decomposition algorithm is able to optimize effectively the joint space trajectory. It has been tested and demonstrated in simulation. Originality/value -A new RR algorithm is introduced for the six-rotation-axis industrial robot performing welding tasks. A new kinetostatic performance index is proposed on evaluating the kinematic quality of robotic postures. It can also be used in other applications like milling, deburing and many other tasks requiring less than 6-DOF in tool frame.

A flagellated, bottom-heavy micro-organism's swimming direction in a shear flow is determined from a balance between the gravitational and viscous torques (gyrotaxis). Hitherto, the cell has been assumed to be a spheroid and the flagella have been neglected. Here we use resistive-force theory to calculate both the magnitude and the direction of a biflagellate cell's swimming velocity and angular velocity relative to the fluid when there is an arbitrary linear flow far from the cell. We present an idealized model for the flagellar beat but, in calculating the velocity of the fluid relative to an element of a flagellum, the presence of the cell body is not neglected. Results are given for the case of a spherical cell body whose flagella beat in a vertical plane, when the ambient linear flow is in the same vertical plane. Results show that resistive-force theory can be used for organisms where the cell body has significant effect on the flow past the flagella and that the viscous torque on the flagella is a significant term in the torque balance equations. A model is presented for the calculation of a cell's velocity and angular velocity in a shear flow which is valid up to high magnitudes of rate of strain or vorticity. The main application of the results will be to modify a recent continuum model for suspensions of gyrotactic micro-organisms (Pedley & Kessler 1990).