Spatial rolling contact pair with a hybrid elastic constraint composed of flexible bands and linear springs

Abstract

Spatial rolling contact pair (SRCP) is a kinematic pair of which two links in contact at a line can generate the relative rolling motion along the specified spatial trajectory. By introducing the SRCP into a linkage mechanism with a single degree-of-freedom (DOF), the mechanism can completely generate the specified output motion. However, the conventional constraint method between two links of the SRCP is not strong enough. In order to enforce the connection between the two links, the novel design of the SRCP which has a hybrid elastic constraint with flexible bands and linear springs is proposed. Since flexible bands and linear springs can suppress slippage and separation between the two links, the SRCP can generate the ideal rolling motion. At first, the design methodology of the rolling contact surfaces of the SRCP, which has been proposed by the authors, is reviewed. Next, it is confirmed that constraint with flexible bands can be applied to the designed surfaces with a mathematical approach. In addition, the design methodology of the flexible bands to generate the zero torque around the contact line between the two links is described. Then, the design methodology for the constraint with linear springs is proposed. In this methodology, linear springs are optimally arranged between links so that two links in the SRCP can keep in contact at a line. Some examples of path generators with the SRCP are designed with the proposed design methodology, and it is confirmed that the SRCPs can generate the ideal rolling motion by some simulations. Finally, the designed examples are fabricated and examined to confirm the validity of the proposed design methodology.

Development of the active spatial rolling contact pair to generate the specified trajectory

“…By using the transmission index for parallel wire-driven mechanisms, active elastic elements are optimally arranged between the links of the SRCP, of which rolling contact surfaces and flexible bands are designed by the methods proposed in the previous work (Kimura et al, 2019). Here, the optimization problem is formulated.…”

“…When the two links of the SRCP keep in line contact, it can be assumed that five independent translation forces are acting at edges of the contact segment between the links. Their direction vectors can be obtained by using the position vector of the rolling contact surface s 1 (t, u), which is derived by the method proposed in the previous work (Kimura et al, 2019), as follows.…”

“…Note that the representation of the design space on Σ j is sometimes not useful because the shape of the SRCP is possible to be complex. Therefore, the design space is specified according to the rolling contact surfaces between the links as shown in the method to optimally arrange linear springs between the links in the previous work (Kimura et al, 2019). Fig.…”

“…Therefore, the magnitudes of cable tensions f a are calculated with an optimization problem to maximize the stability of the rolling contact between the links. In previous work (Kimura et al, 2019), two criteria µ q and y q,ZMP to evaluate the stability of the rolling contact in the SRCP have been proposed. µ q is a criterion to evaluate whether slippage and separation between the links occur or not.…”

“…In order to generate the specified spatial motion with a higher pair-link mechanism, the authors developed the "spatial rolling contact pair (SRCP)", which can completely generate the specified trajectory, as shown in Fig. 1 (Kimura et al, 2019). It is a 1-DOF kinematic pair of which two links in contact at a line roll relatively.…”