During impact the relative motion of two bodies is often taken to be simply represented as half of a damped sine wave, according to the Kelvin-Voigt model. This is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating. Furthermore, it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube, as can be deduced from Goldsmith’s work. A damping term λxnx˙ is here introduced; for a sphere impacting a plate Hertz gives n = 3/2. The Kelvin-Voigt model is shown to be approximated as a special case deducible from this law, and applicable when impacts are absent. Physical experiments have confirmed this postulate.

An alternative is here put forward to counterbalance the present-day preoccupation with series-actuated robot-arms. A systematic study of robots and manipulators, now concentrating on “in-parallel” actuator-arrangements, reveals many geometries applicable either to entire robot-arms or to parts of otherwise series-actuated arms. No survey of this kind is possible without drawing heavily on the theory of screw systems. Having established a means of enumerating possible geometries, screw theory is again invoked to highlight, in broad terms, the patterns considered to be most promising. Criteria for avoiding undesirable robot-arm-configurations are touched upon, and certain aspects of the performance of in-parallel-actuated robot-arms are compared and contrasted with those of series-actuated arms. Within the bounds here set (thought to be realistic) the survey on its own is intended to be exhaustive, but many details remain to be investigated. This paper aims to do no more than edge open the door a little further towards in-parallel actuation in robot-arms; others may then consider that further study could be productive.

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The theory here expounded reveals certain inescapable geometrical conditions with which all couplings must comply when they are required to reproduce at the output shaft, simultaneously and precisely, all angular input shaft displacements. Plunging-type linkage couplings, whose geometrical forms follow very simply from the theory, are fully listed for both intersecting and parallel shafts. Many, particularly those for parallel shafts, are entirely new, and it is believed that there could be useful precision-engineering applications.