• Smart Structures and Systems
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• v.13 no.4
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• pp.711-730
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• 2014

In this paper the system dynamic influences in actuators with variable stiffness as contemporary used in robotics for safety and efficiency reasons are investigated. Therefore, different configurations of serial and parallel elasticities are modeled by dynamic equations and linearized transfer functions. The latter ones are used to identify the characteristic behavior of the different systems and to study the effect of the different elasticities. As such actuation concepts are often used to reach energy-efficient operation, a power consumption analysis of the configurations is performed. From the comparison of this with the system dynamics, strategies to select and control stiffness are derived. Those are based on matching the natural frequencies or antiresonance modes of the actuation system to the frequency of the trajectory. Results show that exclusive serial and parallel elasticity can minimize power consumption when tuning the system to the natural frequencies. Antiresonance modes are an additional possibility for stiffness control in the series elastic setup. Configurations combining both types of elasticities do not provide further advantages regarding power reduction but an input parallel elasticity might enable for more versatile stiffness selection. Yet, design and control effort increase in such solutions. Topologies incorporating output parallel elasticity showed not to be beneficial in the chosen example but might do so in specific applications.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.631-637
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• 2005

This paper presents a stiffness analysis method for a low-DOF parallel manipulator, which takes into account of elastic deformations of joints and links. A low-DOF parallel manipulator is defined as a spatial parallel manipulator which has less than six degrees of freedom. Differently from the case of a 6-DOF parallel manipulator, the serial chains in a low-DOF parallel manipulator are subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each limb can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness model of an F-DOF parallel manipulator consists of F springs related to the reciprocal screws of actuations and 6-F springs related to the reciprocal screws of constraints, which connect the moving platform to the fixed base in parallel. The $6{times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints. The six spring constants can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; the link can be considered as an Euler beam and the stiffness matrix of rotational or prismatic joint can be modeled as a $6{times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is zero. By summing the elastic deformations in joints and links, the compliance matrix of a serial chain is obtained. Finally, applying the reciprocal screws to the compliance matrix of a serial chain, the compliance values of springs can be determined. As an example of explaining the procedure, the stiffness of the Tricept parallel manipulator has been analyzed.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.4
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• pp.320-328
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• 2007

This paper presents a stiffness modeling of a low-DOF parallel robot, which takes into account of elastic deformations of joints and links, A low-DOF parallel robot is defined as a spatial parallel robot which has less than six degrees of freedom. Differently from serial chains in a full 6-DOF parallel robot, some of those in a low-DOF parallel robot may be subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each serial chain can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness of an F-DOF parallel robot can be modeled such that the moving platform is supported by 6 springs related to the reciprocal screws of actuations (F) and constraints (6-F). A general $6{\times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints, The compliance of each spring can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; a link is modeled as an Euler beam and the compliance matrix of rotational or prismatic joint is modeled as a $6{\times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is infinite. By summing joint and link compliance matrices with respect to a reference frame and applying unit reciprocal screw to the resulting compliance matrix of a serial chain, the compliance of a spring is determined by the resulting infinitesimal displacement. In order to illustrate this methodology, the stiffness of a Tricept parallel robot has been analyzed. Finally, a numerical example of the optimal design to maximize stiffness in a specified box-shape workspace is presented.