Kinematics analysis of 6-DOF parallel micro-manipulators with offset u-joints : a case study

This paper analyses the kinematics of a special 6-DOF parallel micro-manipulator with offset RR-joint configuration. Kinematics equations are derived and numerical methodologies to solve the inverse and forward kinematics are presented. The inverse and forward kinematics of such robots compared with those of 6-UCU parallel robots are more complicated due to the existence of offsets between joints of RR-pairs. The characteristics of RR-pairs used in this manipulator are investigated and kinematics constraints of these offset U-joints are mathematically explained in order to find the best initial guesses for the numerical solution. Both inverse and forward kinematics of the case study 6-DOF parallel micro-manipulator are modelled and computational analyses are performed to numerically verify accuracy and effectiveness of the proposed methodologies

Laser-based sensing, measurement, and misalignment control of coupled Linear and angular motion for ultrahigh precision movement

This paper presents a novel methodology for position and orientation (pose) measurement of stages used for micro/nano positioning which produce coupled motions with three planar degrees of freedom (DOF). In the proposed methodology, counter-rotation of the entire mechanism prevents the misalignment of the measurement beams within a laser-interferometry-based sensing and measurement technique. To detect such a misalignment, a sensing strategy constructed around a position sensitive diode has been developed. A feedforward-feedback compound controller has been established to provide the necessary counter-rotation input to reduce the misalignment error. Experimental validation has been conducted through the measurement of the workspace of a three-DOF planar micro/nano positioning stage. Experimental results demonstrate the capability of the technique to provide combined linear/angular measurement

Development of a passive compliant mechanism for measurement of micro/nano-scale planar three DOF motions

This paper presents the design, optimization, and computational and experimental performance evaluations of a passively actuated, monolithic, compliant mechanism. The mechanism is designed to be mounted on or built into any precision positioning stage which produces three degree of freedom (DOF) planar motions. It transforms such movements into linear motions which can then be measured using laser interferometry based sensing and measurement techniques commonly used for translational axes. This methodology reduces the introduction of geometric errors into sensor measurements, and bypasses the need for increased complexity sensing systems. A computational technique is employed to optimize the mechanism’s performance, in particular to ensure the kinematic relationships match a set of desired relationships. Computational analysis is then employed to predict the performance of the mechanism throughout the workspace of a coupled positioning stage, and the errors are shown to vary linearly with the input position. This allows the errors to be corrected through calibration. A prototype is manufactured and experimentally tested, confirming the ability of the proposed mechanism to permit measurements of three DOF motions

Direct kinematics and analytical solution to 3RRR parallel planar mechanisms

This paper presents the direct kinematic solutions to 3DOF planar parallel mechanisms. Efforts to solve the direct kinematics of planar parallel mechanisms have concentrated on RPR mechanisms due to its inherent simplicity. It is established that the direct kinematic equations of a general 3DOF planar parallel mechanism can be reduced to a univariate polynomial of degree 8. This paper presents the derivation of this univariate polynomials for both 3RRR and 3RPR mechanisms, showing the similarities and differences between the two common configurations of 3DOF planar parallel mechanisms. This paper also presents the on the direct kinematic solution to a simplified case of the 3RRR planar parallel mechanisms, where it is possible to decouple the polynomial further into two quadratic equations, describing the position and orientation of the end-effector, respectively. This result will provide an efficient computation method for a very useful configuration of planar parallel manipulators

Robust motion tracking control of piezoelectric actuation systems

This paper proposes a robust control methodology for piezoelectric actuation systems to track specified motion trajectories. This is motivated by the search for an effective control strategy to deal with the problem of nonlinear behaviour in the piezoelectric actuation systems. The basic concept associated with this approach lies in the specification of a target performance and the formulation of a robust control scheme for the system to ensure the convergence of the position tracking error to zero in the presence of parametric uncertainties and hysteresis effect inclusive of other un-modelled disturbances. Stability of the control system is proven theoretically and the robust control methodology is demonstrated to possess a promising tracking ability through the control experiments. Implementation of the control law requires only a knowledge of the estimated parameters and their corresponding bounds as well as the bound of the hysteresis effect including disturbances. Being capable of handling uncertainties and disturbances, the robust control methodology is very attractive in the field of micro/nanomanipulation in which high-precision control applications could be realised

Special class of positive definite functions for formulating adaptive micro/nano manipulator control

This paper presents a special class of positive definite functions for the formulation of adaptive control strategies, specifically in the research of an effective control algorithm for piezoelectric actuation systems in micro/nano manipulation. To deal with the control problems of unknown system parameters, nonlinear hysteresis effects, and disturbances in the piezoelectric actuation systems, an adaptive control methodology is proposed. Using the saturation function derived from a positive definite function to formulate the control methodology, the closed-loop system stability can be guaranteed. Furthermore, the control methodology is proposed to track a desired motion trajectory in position, velocity, and acceleration. In this paper, a special positive definite function is introduced and a control formulation as well as a stability analysis is detailed. Implementation of the control methodology is practical and requires only a knowledge of the initial estimate of the system parameters. In this study, control experiments conducted using the proposed control approach on a piezoelectric actuation system has demonstrated a promising ability in tracking a specified motion trajectory. With this control capability in the presence of unknown system parameters, hysteresis, and external disturbance, the adaptive methodology is very attractive in the field of micro/nano manipulation in which high performance control applications could be realised