On the synthesis of spatial revolute—revolute—spherical—cylindrical motion generators with prescribed coupler loads

Abstract

This work extends the concepts and methodologies of Shen et al. for the synthesis of spherical four-bar motion generators to the synthesis of spatial revolute-revolute-sphericalcylindrical (RRSC) motion generators with applied coupler loads. A constraint that includes coupler loads and driver static torques for the RRSC mechanism is formulated using the principle of virtual work. This constraint is combined with the conventional constraints for the R-R and C-S dyads to form a non-linear optimization problem from which RRSC mechanism solutions are calculated that approximate prescribed coupler poses and satisfy prescribed driver static torques for given coupler loads. The formulated RRSC coupler load and driver static torque constraint are also incorporated in a simplified RRSC motion generation model to form a simplified non-linear optimization problem for calculating RRSC mechanism solutions. This work demonstrates both the conventional and simplified non-linear optimization problems. mechanism utilizes basic joint types (revolute, spherical, and cylindrical only) and requires no strict link and joint configuration conditions to ensure proper assembly and motion, it is one of the most basic spatial, four-bar, and single DOF kinematic chains. The simplicity of the RRSC mechanism coupled with its ability to exhibit spatial motion makes the RRSC mechanism a potential candidate for tasks that are redundant and include a degree of continuous spatial motion.

Revolute-Cylindrical-Cylindrical-Cylindrical linkage optimum dimensional synthesis with static structural loading

“…While optimization models have already been presented for RRSS, RRSC, and 4R Spherical motion generation with static structural loading, the scale of the RCCC linkage is substantially greater than those noted. 14–17 The scale of the RCCC optimization model introduces implementation challenges (using the SQP method in Matlab on a 64 bit Windows laptop) not encountered with the RRSS, RRSC, and 4R Spherical optimization models. For example, in comparison to the 51 unknowns calculated for the RCCC linkage in 5-position motion generation in Table 2, the same problem for the RRSS or 4R Spherical optimization models have only 26 unknowns.…”

“…For example, in comparison to the 51 unknowns calculated for the RCCC linkage in 5-position motion generation in Table 2, the same problem for the RRSS or 4R Spherical optimization models have only 26 unknowns. 14–17 As a result of the scale difference between the models, those for the RRSS, RRSC, and 4R Spherical linkages can practically accommodate greater numbers of precision positions or precision points while the RCCC optimization models encounter the computing limits explained in the previous section.…”

“…Such optimization models have already been introduced for the 4 Revolute Spherical (or 4R Spherical) linkage, the Revolute-Revolute-Spherical-Spherical (or RRSS) linkage and the Revolute-Revolute-Spherical-Cylindrical (or RRSC) linkage. 14–17 No such optimization model has been presented for the RCCC linkage until now.…”