The lack of haptic feedback has negatively affected the surgeon's ability to palpate and diagnose tissue and differentiate its stiffness during surgical operations with commercially available robotic assisted surgical systems. A modular surgical instrument capable of non-invasive measurement of sideways tip/tissue interaction forces for direct application in robotic assisted minimally invasive surgery systems is presented in this paper. The proposed force measurement technique enables the actual non-invasive measurement of the sideways interaction forces at the tip jaws. The instrument has two actuation degrees of freedom (DOF) for the tip operation and grasping orientation. The tip functionality type (e.g., grasping, cutting, and dissecting) can also be changed quickly and easily. Experiments were conducted to evaluate functionalities of the proposed instrument in palpating tissues. The results are presented and analysed here that verify the capability of the proposed instrument in accurately measuring lateral tip/tissue interaction forces.

This paper presents a modular design for a robot-assisted biological cell microinjection system. The proposed design is composed of injection, vision, force measurement and control units that provides sufficient flexibility to observe and control cell microinjection by monitoring and regulating position and force simultaneously. Methodologies have been presented for automation of the laborious tasks associated with microinjection to improve the repeatability and reliability of the process. The system is capable of automatic positioning and focusing of the microcapillary tip as well as automatic realization of the cell piercing during the microinjection process with vision-based approaches. The proposed methods were tested for 100 zebrafish embryos micromanipulation experiments at Blastula stage. 97% success rate was achieved which shows high capability of the proposed design and methods.

This paper presents experimental analysis of laser interferometry-based closed-loop robust motion tracking control for flexure-based four-bar micro/nano manipulator. To enhance the accuracy of micro/nano manipulation, laser interferometry realized robust motion tracking control is established with the experimental facility. This paper contains brief discussions about the error sources associated with the laser interferometry-based sensing and measurement technique, along with detailed error analysis and estimation. Comparative error analysis of capacitive position sensor-based system and laser interferometry-based system is also presented. Robust control demonstrates high precision and accurate motion tracking of the four-bar flexure-based mechanism. The experimental results demonstrate precise motion tracking, where resultant closed-loop position tracking error is of the order of ± 20 nm, and a steady-state error of about ±10 nm. With the experimental study and error analysis, we offer evidence that the laser interferometry-based closed-loop robust motion tracking control can minimize positioning and tracking errors during dynamic motion.

In this paper a 6-RRCRR parallel robot assisted minimally invasive surgery/microsurgery system (PRAMiSS) is introduced. Remote centre-of-motion (RCM) control algorithms of PRAMiSS suitable for minimally invasive surgery and microsurgery are also presented. The programmable RCM approach is implemented in order to achieve manipulation under the constraint of moving through the fixed penetration point. Having minimised the displacements of the mobile platform of the parallel micropositioning robot, the algorithms also apply orientation constraint to the instrument and prevent the tool tip to orient due to the robot movements during the manipulation. Experimental results are provided to verify accuracy and effectiveness of the proposed RCM control algorithms for minimally invasive surgery.

This paper presents a novel unified modelling approach using Bond Graphs (BG) as a graphical language and as a framework for modelling and validation for UAVs. The proposed framework supports a concurrent design approach across the domains. In addition, it doubles as a design and knowledge framework for physical systems at various levels of abstraction. This framework can be used as a tool to facilitate design refinement from behavioural and functional modelling to explore system architecture and for rapid prototyping of mechatronic systems such as UAVs. The model framework was applied to a R-50 experimental model helicopter for obtaining preliminary results.

This paper presents the dynamic modelling and performance evaluation methodologies of a flexure-base mechanism for ultra-precision grinding operations. The mechanical design of the mechanism is briefly described. A piezoelectric actuator is used to drive the moving platform. A flexure-based structure is utilized to guide the moving platform and to provide preload for the piezoelectric actuator. By simplifying the Hertzian contact as a linear spring and damping component, a bilinear dynamic model is developed to investigate the dynamic characteristics of the flexure-based mechanism. Based on the established model, the separation phenomenon of the moving platform from the piezoelectric actuator is analyzed. The influence of the control voltage on the maximum overshoot is also investigated. The slope and cycloidal command signals are used to reduce and/or avoid the overshoot of such flexure-based mechanism under step command signal actuation condition. The effects of the rising time of the command signals on the maximum overshoot and the settling time are studied.

This paper presents a robust methodology for constrained motion tracking control of piezo-actuated flexure-based four-bar micro/nano manipulation mechanisms. This unique control approach is established for the tracking of desired motion trajectories in a constrained environment exhibiting some degree of uncertain stiffness. The control methodology is also formulated to accommodate not only the parametric uncertainties and unknown force conversion function, but also nonlinearities including the hysteresis effect and external disturbances in the motion systems. In this paper, the equations for the dynamic modelling of a flexure-hinged four-bar micro/nano manipulation mechanism operating in a constrained environment are established. A lumped parameter dynamic model that combines the piezoelectric actuator and the micro/nano manipulation mechanism is developed for the formulation of the control methodology. Stability analysis of the proposed closed-loop system is conducted, and the convergence of the motion tracking errors is proven theoretically. Furthermore, precise motion tracking ability in following a desired motion trajectory is demonstrated in the experimental study. This robust constrained motion tracking control methodology is very useful for the development of high performance flexure-based micro/nano manipulation applications demanding high-precision motion tracking with force sensing and feedback.

This paper presents a robust neural network motion tracking control methodology for piezoelectric actuation systems employed in micro/nanomanipulation. This control methodology is proposed for tracking of desired motion trajectories in the presence of unknown system parameters, nonlinearities including the hysteresis effect and external disturbances in the control systems. In this paper, the related control issues are investigated, and a control methodology is established including the neural networks and a sliding control scheme. In particular, the radial basis function (RBF) neural networks are chosen for function approximations. The stability of the closed-loop system, as well as the convergence of the position and velocity tracking errors to zero, is assured by the control methodology in the presence of the aforementioned conditions. An offline learning procedure is also proposed for the improvement of the motion tracking performance. Precise tracking results of the proposed control methodology for a desired motion trajectory are demonstrated in the experimental study. With such a motion tracking capability, the proposed control methodology promises the realization of high-performance piezoelectric actuated micro/nanomanipulation systems.

This paper presents a vision-based approach for valid assessment of surface roughness in both micro-scale and nano-scale regions. To enable data comparisons, three sets of surface data in the micro and nano regions are acquired by using a CCD camera, a video-based optical microscope and a stylus instrument. Data filtering and analysis procedures are applied to the acquired data. Results for computation of roughness parameters by using vision data provide adequate values for assessment of surface roughness in the manner as similar as stylus based technique. No obvious changes in the computed roughness parameter values are resulted from the micro and nano regions. In the nano region, a cavity graphs technique provides distinguishable forms of graphs that tend to more gradual increase of the cavity percentage to denote the collection of the macro surface details. In addition, an auto correlation technique applied in the nano region succeeds to discriminate the surface irregularities relationship with respect to their periodicity and randomness. The overall acquired results indicate that vision systems are a valid source of data for reliable surface roughness evaluation in both micro/nano-scale regions. The results are very useful in achieving commercial 3D vision based micro-nano roughness measurement systems for industrial applications.

This paper investigates the feasibility of a neural network motion control methodology applied in the piezoelectric actuation systems for micro/nano manipulation. This control methodology is proposed for tracking desired motion trajectories in the presence of unknown system parameters, non-linearities including the hysteresis effect, and external disturbances in the micro/nano manipulation systems. The advantage of this control methodology is that no prior knowledge of the system parameters, or of the initial estimates of the neural networks, is required for the physical realisation of the control system. Simulation results of the control methodology for tracking a desired motion trajectory are presented. This control methodology can be utilised to realise high performance micro/nano manipulation systems driven by piezoelectric actuators.

This paper presents the forward kinematics and stiffness estimation methodologies of a flexure-based five-bar micro-manipulator. The mechanical design of the micro-manipulator is firstly descried. Base on the configuration of the proposed flexure-based micro-manipulator, the whole system has been divided into a five-bar parallel mechanism and an amplification mechanism. Two mathematical expressions describing the path traced by the tips of two passive links connected to each other are obtained. The Cartesian coordinates of the end-effector attached to one of the passive links is obtained according to the geometric relationship. The amplification factor of the lever mechanism is also derived based on the analytical solution of the four-bar linkage. By simplifying the flexure hinge as an ideal revolution joint with a linear torsional spring, the stiffness of the compliant five-bar mechanism is derived in both actuation and Cartesian spaces. It is noted that the stiffness of the compliant five-bar mechanism is positional dependant, and reaches up to infinite value at the singular configuration.

Fully automated microassembly procedure has become an essential subject of interest among microsystem researchers due to the promising potential of the establishment of fully functional Micro Electro Mechanical System (MEMS) devices and significant cost reduction on large number of consumer based products once the system is realized. In the heart of microassembly, the development of high precision micrograsping technique for dexterous manipulation of minute parts becomes the key factor which determines the success of microassembly process. This paper presents the development of a microgripper for the purpose of manipulating micro sized objects in precision environment. The gripper is realized based on compliant mechanism concept that uses flexure hinge to replace the traditional rigid hinge due to its favorable advantages of eliminating the backlash and coulomb friction problems. Modeling of this gripper was performed utilizing a combination of Pseudo Rigid Body Model (PRBM) and Finite Element Analysis (FEA) which effectively accelerates the prototyping procedure. The gripper was cut out of aluminum plate using electro-discharge machining (EDM) technique and experimental studies were conducted to investigate the performance as well as for model verification. The result between experiment and computational analysis has shown high degree of agreement. High displacement amplification was successfully recorded and maximum stroke of 100 mum can be achieved.

This paper addresses the problem of certifying the performance of a precision flexure-base mechanism design with respect to the given constraints. Due to the stringent requirements associated with the applications of flexure-based precision mechanisms, it is necessary to be able to evaluate and certify the performance at the design stage, taking into account the possible sources of errors: such as fabrication tolerance and modeling inaccuracies in flexure joints. An interval-based method is proposed to certify whether various constraints are satisfied for all points within a required workspace. This paper presents the interval-based methodology and its implementation on a planar 3RRR parallel flexure-based manipulator.

This paper presents the issues associated with the mobile robot navigation and the establishment of a new technique to navigate the mobile robot in a real world environment. The issues discussed are (i) If multiple obstacles are appeared in the environment with equal distances as perceived from multiple sensors of robot, then the corresponding multiple obstacles are treated as a whole and the robot deviate from obstacles widely and avoid then reaching to the target. As a result of the wide deviation, the robot takes long time and long path to reach the target position. (ii) Behavior rule selection when multiple obstacles are appeared in the environment with equal distances from robot. The robot navigation with optimal path, time and rule selection are more important and critical task, whenever the mobile robots are engaged to search the lives in the event of natural disaster like earthquake etc. A new methodology is proposed and used for resolving the above issues and discussed in this paper. The mathematical aspect of resolving conflicts is presented the following section.

The mobile robot navigation with complex environment needs more input space to match the environmental data into robot outputs in order to perform realistic task. At the same time, the number of rules at the rule base needs to be optimized to reduce the computing time and to provide the possibilities for real time operation. In this paper, the optimization of fuzzy rules using a modified fuzzy associative memory (MFAM) is designed and implemented. MFAM provides good flexibility to use multiple input space and reduction of rule base for robot navigation. This paper presents the MFAM model to generate the rule base for robot navigation. The behavior rules obtained from MFAM model are tested using simulation and real world experiments, and the results are discussed in the paper and compared with the existing methods.

This paper presents a robust adaptive control methodology for piezoelectric actuation systems to track specified motion trajectories. This methodology is proposed to deal with the control problems of unknown or uncertain system parameters, nonlinearities including the hysteresis effect, and external disturbances in the piezoelectric actuation systems, without any form of feed-forward compensation. In this paper, a special class of positive definite functions is employed to formulate the control methodology such that the closed-loop system stability can be guaranteed. The control formulation as well as the stability analysis is detailed. Furthermore, an experimental investigation is also conducted. Implementation of the control methodology is practical as only a knowledge of the estimated system parameters is required. In the experimental study, a promising tracking ability in following a specified motion trajectory is demonstrated. With the capability of motion tracking under the aforementioned conditions, the robust adaptive control methodology is very attractive in realising high performance control applications in the field of micro/nano manipulation.

This work presents chemical communication techniques for nanorobots foraging in fluid environments relevant for medical applications. Unlike larger robots, viscous forces and rapid diffusion dominate their behaviors. Examples range from modified microorganisms to nanorobots using ongoing developments in molecular computation, sensors and motors. The nanorobots use an innovative methodology to achieve decentralized control for a distributed collective action in the combat of cancer. A communication approach is described in the context of recognize a single tumor cell in a small venule as a target for medical treatment. Thus, a higher gradient of signal intensity of E-cadherin is used as chemical parameter identification in guiding nanorobots to identify malignant tissues. A nanorobot can effectively use chemical communication to improve intervention time to identify tumor cells

This paper proposes and evaluates an adaptive technique and a variable structure control approach for piezoelectric actuation systems to track specified motion trajectories. The proposed control methodologies are formulated to accommodate unknown or uncertain system parameters, nonlinearities including the hysteresis effect, and external disturbances in the piezoelectric actuation systems without any form of feed-forward compensation. In this study, both control methodologies are demonstrated to possess a promising motion tracking ability experimentally. In comparison, the variable structure control approach is evaluated to be superior to the adaptive technique in the motion tracking control. With the ability to track motion trajectories under parametric uncertainties, nonlinearities, and external disturbances, the proposed control methodologies are very attractive in realising the high-precision piezoelectric actuation systems for micro/nano manipulation

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

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

This paper presents a new methodology to simulate soft object deformation by drawing an analogy between a cellular neural network (CNN) and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by a nonlinear CNN. The novelty of the methodology is that: 1) CNN techniques are established to describe the potential energy distribution of the deformation for extrapolating internal forces and 2) nonlinear materials are modeled with nonlinear CNNs rather than geometric nonlinearity. Integration with a haptic device has been achieved for deformable object simulation with force feedback. The proposed methodology not only predicts the typical behaviors of living tissues, but it also accommodates isotropic, anisotropic, and inhomogeneous materials, as well as local and large-range deformation.

Piezoelectric actuators (PEA) are the fundamental elements for high-precision high-speed positioning/tracking task in many nanotechnology applications. However, the intrinsic hysteresis observed in PEAs has impaired their potential, specially, the motion accuracy. In this paper, the complicated nonlinear dynamics of PEA including hysteresis, creep, drift and time-delay etc. are treated as a black-box system exhibited as rate-dependent hysteresis. The multi-valued hysteresis is analyzed as a single-valued function so that a neural network (NN) can be built to model the hysteresis and its inversion. A sliding mode controller (SMC) augmented with inverse hysteresis model is then developed to compensate the hysteretic behavior, modeling error and disturbance to improve the positioning/tracking stability and accuracy. The effectiveness of this algorithm experimentally verified through the actual tracking control of a PEA.

This paper presents a new methodology for the deformation of soft objects by drawing an analogy between heat conduction and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by the principle of heat conduction. An improved heat conduction model is developed for propagating the energy generated by the external force in a natural manner. A method is presented to derive the internal forces from the potential energy distribution. This methodology not only deals with large-range deformation, but also accommodates both isotropic and anisotropic materials by simply changing thermal conductivity constants. Examples are presented to demonstrate the efficiency of the proposed methodology.

This paper presents the enhanced stiffness modeling and analysis of robot manipulators, and a methodology for their stiffness identification and characterization. Assuming that the manipulator links are infinitely stiff, the enhanced stiffness model contains: 1) the passive and active stiffness of the joints and 2) the active stiffness created by the change in the manipulator configuration, and by external force vector acting upon the manipulator end point. The stiffness formulation not accounting for the latter is known as conventional stiffness formulation, which is obviously not complete and is valid only when: 1) the manipulator is in an unloaded quasistatic configuration and 2) the manipulator Jacobian matrix is constant throughout the workspace. The experimental system considered in this study is a Motoman SK 120 robot manipulator with a closed-chain mechanism. While the deflection of the manipulator end point under a range of external forces is provided by a high precision laser measurement system, a wrist force/torque sensor measures the external forces. Based on the experimental data and the enhanced stiffness model, the joint stiffness values are first identified. These stiffness values are then used to prove that conventional stiffness modeling is incomplete. Finally, they are employed to characterize stiffness properties of the robot manipulator. It has been found that although the component of the stiffness matrix differentiating the enhanced stiffness model from the conventional one is not always positive definite, the resulting stiffness matrix can still be positive definite. This follows that stability of the stiffness matrix is not influenced by this stiffness component. This study contributes to the previously reported work from the point of view of using the enhanced stiffness model for stiffness identification, verification and characterization, and of new experimental results proving that the conventional stiffness matrix is not complete and is valid under certain assumptions.

This paper presents a methodology for optimum dynamic balancing of planar parallel manipulators typified with a variable speed 2 DOF parallel manipulator articulated with revolute joints. The dynamic balancing is formulated as an optimisation problem such that a sum-squared values of bearing forces, driving torques, shaking moment, and the deviation of the angular momentum from its mean value are minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of the shaking force balancing conditions, the sizes of some inertial and geometric parameters are satisfied. Sets of optimisation results corresponding to various combinations of the elements of the objective function are evaluated in order to quantify their influence on the resulting bearing forces, the driving torques, shaking moment and force. The results prove that the proposed optimisation approach can be used to minimize any desired combination of the forces, moments, and torques involved in any parallel mechanism by choosing a suitable set of weighting factors. The method is systematic, versatile and easy to implement for the optimum balancing of the parallel manipulator and more general parallel manipulators.

Determining the most appropriate sequence for assembling products requires assessment of the process, product, and the technology applied. Most production engineers apply constraint based evaluation and history to identify the solution sequence. What if their solution is sub-optimal? In this paper a self-learning technique for selecting a sequence and dynamically changing the sequence is presented, selection is based on the history of assemblies. The evaluation is dependent on part properties rather than parts and their relationships, thus no previous knowledge of parts and their interaction is required in the decision making process. The method assumes assembly is without constraint, for example, a highly flexible robotic assembly cell. This maximises the ability of the algorithm to select sequences for new products and optimise them. The heart of the algorithm is a reinforcement-learning model, which punishes failed assembly steps, this facilitates feedback sequence selection, when: current methods are merely feedforward. This feedback approach addresses combinatorial explosion that can cripple assembly planners.

Design for robotic assembly has focused on constraining parts geometry and modularised designs to produce families of products. Constraints of this nature degenerate robot flexibility and fail to design products conducive to flexible robotic assembly and within the capabilities of robots. In this paper design principles addressing the needs of flexible robotic systems are presented. The design of parts plays a significant role in making robot actions less dependent on part shape and sensor fusion. The design principles described here in aim to address several areas of concern; part feeding, robot adaptability, and assembly reliability.

This paper presents a methodology to create 3D visualization of discrete event simulation. This methodology connects discrete event simulation directly to 3D animation with its novel methods of analyzing and converting discrete simulation results into animation events to trigger 3D animation. Discrete simulation results are analyzed and displayed in a graph structure that reveals all possible sequences of simulation events. In addition, a 3D animation framework is constructed for the visualization of discrete simulation results. This framework supports the reuse of both the existing 3D animation objects and behavior components, and allows the rapid development of new 3D animation objects by users with no special knowledge in computer graphics. This methodology has been implemented with the software component technology. Results in an electronics assembly factory are also provided in the paper to demonstrate the feasibility of this approach.

This paper deals with optimum force balancing of a planar parallel manipulator, articulated with revolute joints, by properly distributing link masses, and connecting only one spring between its two coupler links. After conducting the static force analysis of the mechanism, the force balancing is formulated as an optimisation problem such that a sum-squared values of bearing forces is minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of balancing conditions, the sizes of some inertial and geometric parameters are satisfied. Optimisation results indicate that the proposed optimisation approach is systematic, versatile and easy to implement for the optimum balancing of the parallel manipulator and other more general parallel manipulators. This work contributes to previously published work from the point of view of being a step towards optimum design of parallel manipulators, which is currently lacking in the literature.

This paper aims (i) to introduce a new monolithic micromanipulation system for applications requiring micro/nano scale planar motion, and (ii) to model its stiffness consisting of the inherent stiffness of its joints, and the artificial stiffness due to its joint space position controller in order to obtain a decoupled compliant motion for the manipulator end point while a Cartesian force vector is acting upon it. The micromanipulation system is an in-parallel actuated planar manipulator based on five single DOF flexure joints connecting five supposedly rigid links to each other. Numerical results provided show that there exist practical operation ranges of the manipulator yielding both a suitable set of joint serve gains as well as a diagonal Cartesian stiffness matrix. The stiffness model can be used to predict the reaction forces arising from part misalignment and the task forces during the execution of micro tasks, such as micromanufacturing and microassembly. The determination of the forces is also useful for many applications such as designing micro fixtures and micro end effectors sustainable to task forces.

In this paper, we present the results and implications of our experimental study into the parameter identification and the position error modelling of a Motoman SK 120 robot manipulator for kinematic calibration. The true values of the parameters and the coefficients of the error model are estimated, in the least-squares sense, from the position data of 85 identification configurations of the manipulator measured by a high precision laser tracking system. The proposed error model is utilised to calculate the expected position errors for an exemplary Cartesian space trajectory. These errors are then corrected using a first order approximation of the inverse kinematic model. The results prove that the established model is accurate enough to represent position error of the manipulator without needing further experimental position data. This work contributes to previously published work from the point of view of being a simple and systematic approach to the self-calibration of robotics systems with minimum experimental data.

Mechanical hands are not restricted in physical features in the way human hands are. Therefore, we should not be conned into designing mechanical hands or products and their parts on human limitations. A simultaneous and integrated approach to both the gripper and part design maximises the opportunity for the best mechanical outcome. Force closure formed the basis for a class of finger features aimed at selective restraint to satisfy task requirements. This paper evaluates this set of finger features based on engineering criteria, and ranks them. For the analysis it is assumed that the opposable fingers fitted with the same feature type are applied to the grasping task. The elliptical paraboloid, semi-ellipsoidal and hemispherical ranked significantly better than other feature types. Identifying finger features, which satisfy a broad range of tasks, reduces the need for re-tooling, and improves certainty about part location and relative orientation. Aided by the ability to address a broad range of tasks, design rules are established which assimilate grasps to part design. The approach focuses on minimising undesirable wrenches by alignment of grasp location with the centre of wrenches and the centre of gravity.

Current methods for singularity avoidance are analysed through study of the Jacobian minors. It is demonstrated that semi-singular positions, often defined as positions where dexterity decreases, occur as one minor becomes zero and that the only truly, uncontrollable, singular regions occur when all minors are zero. Existing singularity avoidance methods are analysed with attention to the way they deal with semi-singular regions. An 8-Degree Of Freedom (8-DOF) redundant autonomous articulated robot is used to demonstrate the effectiveness of the studied methods. Particular attention is made to the inherent limitations caused by a desire to maintain the aspect (sometimes referred to as configuration) in which the robot is operating. The use of the minors in manipulator analysis is shown to be useful in clarifying what truly occurs when dexterity is lost.