Abstract
Abstract. This contribution shows that a method proposed previously, for the determination of the instantaneous centers of rotation of planar closed chains, can be generalized for the determination of the instantaneous screw axes of general one-degree-of-freedom spatial mechanisms. Hence, the approach presented in this paper can be applied to any of the closed chains that belong to any of the subgroups of the Euclidean group, SE(3), namely planar, spherical or chains associated with the Schönflies subgroups, among others. Furthermore it can be also applied to multi-loop mechanisms and even to closed chains that are exceptional o paradoxical, as indicated by Hervé.
Highlights
In 2016, Kim et al (2016) presented a method for the determination of the instantaneous centers of velocity of planar mechanisms. The basis of their approach is to set up the equations for the solution of the velocity analysis of the mechanism, whose instantaneous centers are to be determined
2ω1 2$1O + 3ω2 3$2O + 4ω3 4$3O + 4ω1 4$1O = 0 5ω2 5$2O + 8ω5 8$5O + 8ω6 8$6O + 6ω3 6$3O − 3ω2 3$2O = 0 8ω7 8$7O + 7ω4 7$4O − 4ω3 4$3O − 6ω3 6$3O − 8ω6 8$6O = 0 (6). This is the equation used in the velocity analysis of the indeterminate planar mechanism dealt with in Sect. 3.1 and it is the basic equation for solving the velocity analysis of any multi-loop mechanism
In order to carry out the velocity analysis, it is necessary to determine the screws associated with the kinematic pairs, all of them revolute pairs, with respect to the origin of the coordinate system, O
Summary
In 2016, Kim et al (2016) presented a method for the determination of the instantaneous centers of velocity of planar mechanisms. It will be shown that once the velocity analysis of an arbitrary linkage – planar, spherical, spatial or associated to any other subgroup of the Euclidean group, SE(3), determinate or indeterminate – is solved, there is an easy process to determine the instantaneous screw axes, ISA, for its initials in English, or the corresponding simplification; i.e. the instantaneous rotation pole for spherical linkages or the instantaneous velocity center for planar linkages It can handle, single or multi-loop kinematic chains regardless if they are determined or undetermined, even exceptional and paradoxical linkages, see Hervé (1978). Some applications of the instantaneous screw axes, or their counterparts, in the case of planar and spherical linkages, can be found in Zhao and Zhou (2004), Di Gregorio (2007) and Zarkandi (2011)
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