A General Static Torque Constraint for Spatial Four-Bar Motion Generation With a Coupler Load

Abstract

A general static torque constraint for spatial four-bar mechanisms with coupler forces is formulated in this work. With this constraint, the user can synthesize spatial four-bar motion generators that also support static coupler loads. This constraint is demonstrated in the synthesis of RRSS, SSRC, and 4R spherical motion generators to approximate prescribed coupler poses and do so within maximum specified driver torques for given coupler forces.

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.…”

Revisiting Planar Four-Bar Precision Synthesis with Finite and Multiply-Separated Positions

“…Figure 2 includes the parameters (dimensionless) for five gripper poses. Additionally, coupler point velocity magnitudes of 1sec −1 at −30º and 0.5sec −1 at −60º are specified for p 3 and p 5 respectively. A constant crank angular velocity is preferred for the planar four-bar linkage solution as well as order defect elimination.…”

“…The objective in planar four-bar precision synthesis is to calculate the dimensions of a planar four-bar linkage to precisely achieve or approximate prescribed coupler poses in motion generation (2,3) , coupler path points in path generation (4,5) or crank and follower rotation angles in function generation (6,7) . Schaefer and Kramer presented a technique to synthesize planar four-bar path generators to approximate prescribed coupler path points and coupler point velocities (1) .…”