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J. Mechanisms Robotics. 2017;9(6):061003-061003-9. doi:10.1115/1.4037616.

A gravity equilibrator is a statically balanced system which is designed to counterbalance a mass such that any preferred position is eliminated and thereby the required operating effort to move the mass is greatly reduced. Current spring-to-mass gravity equilibrators are limited in their range of motion as a result of constructional limitations. An increment of the range of motion is desired to expand the field of applications. The goal of this paper is to present a compact one degree-of-freedom mechanical gravity equilibrator that can statically balance a rotating pendulum over an unlimited range of motion. Static balance over an unlimited range of motion is achieved by a coaxial gear train that uses noncircular gears. These gears convert the continuous rotation of the pendulum into a reciprocating rotation of the torsion bars. The pitch curves of the noncircular gears are specifically designed to balance a rotating pendulum. The gear train design and the method to calculate the parameters and the pitch curves of the noncircular gears are presented. A prototype is designed and built to validate that the presented method can balance a pendulum over an unlimited range of motion. Experimental results show a work reduction of 87% compared to an unbalanced pendulum and the hysteresis in the mechanism is 36%.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061004-061004-10. doi:10.1115/1.4037800.

This paper proposes a two translational and two rotational (2T2R) four-degrees-of-freedom (DOF) parallel kinematic mechanism (PKM) designed as a knee rehabilitation and diagnosis mechatronics system. First, we establish why rehabilitation devices with 2T2R motion are required, and then, we review previously proposed parallel mechanisms with this type of motion. After that, we develop a novel proposal based on the analysis of each kinematic chain and the Grübler–Kutzbach criterion. Consequently, the proposal consists of a central limb with revolute-prismatic-universal (RPU) joints and three external limbs with universal-prismatic-spherical (UPS) joints. The Screw theory analysis verifies the required mobility of the mechanism. Also, closed-loop equations enable us to put forward the closed-form solution for the inverse-displacement model, and a numerical solution for the forward-displacement model. A comparison of the numerical results from five test trajectories and the solution obtained using a virtual prototype built in msc-adams shows that the kinematic model represents the mechanism's motion. The analysis of the forward-displacement problem highlights the fact that the limbs of the mechanism should be arranged asymmetrically. Moreover, the Screw theory makes it possible to obtain the Jacobian matrix which provides insights into the analysis of the mechanism's workspace. The results show that the proposed PKM can cope with the required diagnosis and rehabilitation task. The results provide the guidelines to build a first prototype of the mechanism which enables us to perform initial tests on the robot.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061005-061005-9. doi:10.1115/1.4037801.

The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric constraints, where a geometric constraint is an algebraically expressed constraint on the pose, pivots, or something equivalent. In addition, we extend it to linear, nonlinear, exact, and approximate constraints. This extension also includes the problems when there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Machine designers often grapple with such problems while designing linkage systems where the constraints are of different varieties and usually imprecise. In this paper, we present (1) a unified approach for solving the extended Burmester problem by showing that all linear and nonlinear constraints can be handled in a unified way without resorting to special cases, (2) in the event of no or unsatisfactory solutions to the synthesis problem, certain constraints can be relaxed, and (3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange multiplier method. We present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061006-061006-12. doi:10.1115/1.4037802.

This paper examines the dynamics of a type of silicon-based millimeter-scale hexapod, focusing on interaction between structural dynamics and ground contact forces. These microrobots, having a 5 mm × 2 mm footprint, are formed from silicon with integrated thin-film lead–zirconate–titanate (PZT) and high-aspect-ratio parylene-C polymer microactuation elements. The in-chip dynamics of the microrobots are measured when actuated with tethered electrical signal to characterize the resonant behavior of different parts of the robot and its piezoelectric actuation. Out-of-chip robot motion is then stimulated by external vibration after the robot has been detached from its silicon tethers, which removes access to external power but permits sustained translation over a surface. A dynamic model for robot and ground interaction is presented to explain robot locomotion in the vibrating field using the in-chip measurements of actuator dynamics and additional dynamic properties obtained from finite element analysis (FEA) and other design information. The model accounts for the microscale interaction between the robot and ground, for multiple resonances of the robot leg, and for rigid robot body motion of the robot chassis in five degrees-of-freedom. For each mode, the motions in vertical and lateral direction are coupled. Simulation of this dynamic model with the first three resonant modes (one predominantly lateral and two predominantly vertical) of each leg shows a good match with experimental results for the motion of the robot on a vibrating surface, and allows exploration of influence of small-scale forces such as adhesion on robot locomotion. Further predictions for future autonomous microrobot performance based on the dynamic phenomena observed are discussed.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2017;9(6):061007-061007-12. doi:10.1115/1.4037805.

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

Commentary by Dr. Valentin Fuster

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