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Abstract Collaborative robots must simultaneously be safe enough to operate in close proximity to human operators and powerful enough to assist users in industrial tasks such as lifting heavy equipment. The requirement for safety necessitates that collaborative robots are designed with low-powered actuators. However, some industrial tasks may require the robot to have high payload capacity and/or long reach. For collaborative robot designs to be successful, they must find ways of addressing these conflicting design requirements. One promising strategy for navigating this tradeoff is through the use of static balancing mechanisms to offset the robot’s self-weight, thus enabling the selection of low-powered actuators. In this paper, we introduce a novel, two degrees-of-freedom static balancing mechanism based on spring-loaded, wire-wrapped cams. We also present an optimization-based cam design method that guarantees the cams stay convex, ensures the springs stay below their extensions limits, and minimizes sensitivity to unmodeled deviations from the nominal spring constant. Additionally, we present a model of the effect of friction between the wire and the cam. Lastly, we show experimentally that the torque generated by the cam mechanism matches the torque predicted in our modeling approach. Our results also suggest that the effects of wire-cam friction are significant for non-circular cams. 

Continuum robots suffer large deflections due to internal and external forces. Accurate modeling of their passive compliance is necessary for accurate environmental interaction, especially in scenarios where direct force sensing is not practical. This paper focuses on deriving analytic formulations for the compliance of continuum robots that can be modeled as Kirchhoff rods. Compared to prior works, the approach presented herein is not subject to the constant-curvature assumptions to derive the configuration space compliance, and we do not rely on computationally-expensive finite difference approximations to obtain the task space compliance. Using modal approximations over curvature space and Lie group integration, we obtain closed-form expressions for the task and configuration space compliance matrices of continuum robots, thereby bridging the gap between constant-curvature analytic formulations of configuration space compliance and variable curvature task space compliance. We first present an analytic expression for the compliance of aingle Kirchhoff rod.We then extend this formulation for computing both the task space and configuration space compliance of a tendon-actuated continuum robot. We then use our formulation to study the tradeoffs between computation cost and modeling accuracy as well as the loss in accuracy from neglecting the Jacobian derivative term in the compliance model. Finally, we experimentally validate the model on a tendon-actuated continuum segment, demonstrating the model’s ability to predict passive deflections with error below 11.5% percent of total arc length. 

Abstract Balancing parallel robots throughout their workspace while avoiding the use of balancing masses and respecting design practicality constraints is difficult. Medical robots demand such compact and lightweight designs. This paper considers the difficult task of achieving optimal approximate balancing of a parallel robot throughout a desired task-based dexterous workspace using balancing springs only. While it is possible to achieve perfect balancing in a path, only approximate balancing may be achieved without the addition of balancing masses. Design considerations for optimal robot base placement and the effects of placement of torsional balancing springs are presented. Using a modal representation for the balancing torque requirements, we use recent results on the design of wire-wrapped cam mechanisms to achieve balancing throughout a task-based workspace. A simulation study shows that robot base placement can have a detrimental effect on the attainability of a practical design solution for static balancing. We also show that optimal balancing using torsional springs is best achieved when all springs are at the actuated joints and that the wire-wrapped cam design can significantly improve the performance of static balancing. The methodology presented in this paper provides practical design solutions that yield simple, lightweight and compact designs suitable for medical applications where such traits are paramount.