Set of manipulating forces in wire driven systems

Optimal Force Generation for an Underconstrained Planar Cable Robot

“…In Shen et al (1994), the total volume of the force set was termed the "force manipulability measure." Figure 6 clearly shows that the redundant system fully OPTIMAL FORCE GENERATION FOR PLANAR CABLE ROBOT 33 Figure 6 Comparison of force generation ability of proposed redundant system and standard fixed geometry system at discrete locations.…”

“…Figures 4b-d show the corresponding cable tensions and cable angles for this location, again illustrating the solution regimes. Figure 5 shows the net force in a polar format and yields a result similar to the "Set of Manipulating Forces" from Shen et al (1994). Figure 5 clearly shows that the addition of the redundant degrees of freedom changes the normally expected shape of the force set to one with six distinct sides as opposed to a four-sided polygon for a typical fixed-geometry system.…”

“…In general, the number of cables employed by a cable robot varies between designs, but to manipulate all the degrees of freedom of the end-effector, at least one more cable than the number of degrees of freedom is required (Shen et al, 1994), i.e., this is the minimum number of cables required to fully constrain a cable robot. Many designs have been built or proposed (both fully constrained and underconstrained) for spanning applications from camera platforms (Thompson and Blackstone, 2005;Rodnunsky, 2006) to advanced cranes (Albus et al, 1993;Yamamoto et al, 1999) and haptic interfaces (Williams, 1998;Zitzewitz et al, 2009).…”

“…The "set of manipulating forces" can be used to evaluate a location in the workspace as an alternative to the more traditional manipulability index frequently seen with rigid link systems (Shen et al, 1994). The workspace itself can be determined by using the wrench-feasible workspace approach for both fully constrained and underconstrained systems (Bosscher et al, 2006).…”

Dynamic trajectory planning study of planar two-dof redundantly actuated cable-suspended parallel robots

“…According to the number of cables and degrees of freedom (dofs), cable-driven parallel robots are divided into three types: redundantly constrained robots (i.e. the number of cables is larger than the dofs [8]), statically determined robots (i.e. the number of cables is equal to the dofs) and underactuated robots (i.e.…”