Variable stiffness design of redundantly actuated planar rotational parallel mechanisms

Variable-stiffness decoupling of redundant planar rotational parallel mechanisms with crossed legs

“…Similarly, as derived from equation (3) and equation (4), the total active stiffness K ua of leg-uncrossed RPRPM resulting from the internal force f u 0 at the initial position is (Li et al., 2017): where, |lu0| is the total length of the legs at the initial position. |lu0|=(ra-rbfalse)2+L0 2.…”

“…Torsional stiffness of RPRPM is defined as the derivative of torque Q with respect to rotating angle q, that is (Chakarov, 1998; Li et al., 2017): …”

“…By substituting equation (2) into equation (1), the stiffness K of RPRPM consists of active stiffness K a resulting from the internal force f 0 and passive stiffness K p caused by the springs compliance k′ of elastic legs (Chakarov, 1999; Li et al., 2017): where active stiffness Ka=f0(∂rT∂qEln+rTE∂ln∂q). Passive stiffness Kp=k'(rTElnfalse)2.…”

“…Similarly, it is derived from equation (3) and equation (4), the total passive stiffness K up of leg-uncrossed RPRPM caused by the spring compliance k u ′ of the elastic legs at the initial position is (Li et al., 2017): …”

“…The stiffness of the redundant mechanism consists of active stiffness resulting from internal forces and passive stiffness caused by compliances of the flexible element (Chakarov, 1999; Li et al., 2017); the initial stiffness is the passive stiffness when the initial internal force is zero. As a stiffness variation index, the stiffness variation multiple is the ratio of the stiffness of the internal force to the initial stiffness of zero internal force, or the reciprocal of the ratio.…”