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Abstract
Underactuated Cable-Driven Parallel Robots ( CDPR ) employ a number of cables smaller than the degrees of freedom ( DoFs ) of the end-effector ( EE ) that they control. As a consequence, the EE is underconstrained and preserves some freedoms even when all actuators are locked, which may lead to undesirable oscillations. This paper proposes a methodology for the computation of the EE natural oscillation frequencies, whose knowledge has proven to be convenient for control purposes. This procedure, based on the linearization of the system internal dynamics about equilibrium configurations, can be applied to a generic robot suspended by any number of cables comprised between 2 and 5. The kinematics, dynamics, stability and stiffness of the robot free motion are investigated in detail. The validity of the proposed method is demonstrated by experiments on 6- DoF prototypes actuated by 2, 3, and 4 cables. Additionally, in order to highlight the interest in a robotic context, this modelling strategy is applied to the trajectory planning of a 6- DoF 4-cable CDPR by means of a frequency-based method (multi-mode input shaping), and the latter is experimentally compared with traditional non-frequency-based motion planners.
Highlights
Cable-driven parallel robots (CDPRs) control the endeffector (EE) pose by means of extendable cables
Start and end configurations are selected near the UACDPR static workspace edges [33], in order to stress the importance of careful trajectory planning so as to avoid potentially dangerous situations, such as cable loss of tension due to platform large oscillatory motions. is expressed by xyz Tait-Bryan angles, since no representation singularities are expected throughout the manipulator static workspace: ζ s = [0.36, −0.82, −0.37, −0.35, 0.51, 0.12]T [m, rad] ζ e = [1.82, 0.55, −0.37, 0.38, −0.25, 0]T [m, rad]
This paper presented a methodology for the computation of the natural oscillation frequencies of underactuated cable-driven parallel robots
Summary
Cable-driven parallel robots (CDPRs) control the endeffector (EE) pose by means of extendable cables. In case the EE is not in a static equilibrium configuration when actuators cease to move, the UACDPR exhibits (possibly dangerous) oscillatory motions This oscillatory behaviour is naturally expected to occur at the end-point of a trajectory, if suitable motion-planning and control techniques are not employed [1], or it may result from an emergency stop or an actuator failure. Despite these drawbacks, the use of CDPRs with a limited number of cables may be favorable in several applications, in which a limitation of mobility is acceptable in order to enhance workspace accessibility or decrease mechanical complexity and robot cost [2]–[5].
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