Flexibility Effects in a Single Link Robotic Manipulator

A single link robotic manipulator is modeled as a rotating flexible beam with a rigid mass at the tip and accurate energy expressions are derived. The resulting partial differential equations are solved using an approximate method of weighted residuals. From the solutions, coupling between axial and flexural deformations and the interactions with rigid body motions are rigorously analyzed. The emphasis in the current paper is not on an exhaustive analysis of existing systems but it is rather intended to compare and highlight the various flexibility effects in a relatively simple system. Hence, a nondimensional parametric analysis is performed to determine the effect of several parameters (including the rotating speed) on the errors and the individual interaction effects are discussed. Comparison with previous work in the field shows important phenomena often ignored or buried in large scale numerical analyses. Future work including application to multi-link robots is outlined.

Kinematics and Dynamics of a Parallel Manipulator With Woven Joints

Presented is an analysis of the kinematics and the inverse dynamics of a proposed three DOF parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangin technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers in order to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline.

Impact Control of Flexible Robots Using Sliding Mode Technique

In the flexible robot force control situations, if there exists a discontinuity between the robot tip sensor and the work-piece, the robot contact process becomes a nonlinear system control problem. The control tasks require the robot hand to switch from free motion control to contact motion control. The inevitable high impact force tends to let the system become unstable. The purpose of this paper is to investigate the control of the manipulator during this process. In this paper, dynamic models of the flexible link manipulator in both non-contacted and contacted modes are first derived. Due to the fact that the arm vibration shape functions are changed between the two modes, a transform matrix will be used to transform the controlled state variables, such as generalized position and velocity. A nonlinear sliding mode control technique has been implemented in an attempt to extinguish the chatter phenomenon and settle quickly to the desired setpoint.

Modeling of a Finger-Follower Cam System With Verification in Contact Forces

A lumped/distributed-parameter, dynamic model is developed to investigate the dynamic responses of a finger-follower valve train with the effects of an oscillating pivot, frictional forces between sliding surfaces, and a hydraulic lash adjuster. Based on the measured force data at low speed, an algorithm is derived to determine the dynamic Coulomb friction coefficients around maximum valve lift simultaneously at three contact points. A constraint equation is formulated to find the contact position between the cam and the follower kinematically. This makes it possible for the model to simulate the dynamic response of the cam system when the pivot is moving. A hydraulic lash adjuster acting as the pivot of the follower is also modeled with the effects of oil compressibility and oil refill mechanism. The model is numerically integrated and shown to have good agreement between simulation results and experimental data of contact forces at three different speeds. The maximum operating speed is limited by valve toss, loss contact between components. The model predicts toss between the hydraulic lash adjuster and the follower at 2535 rpm, and experiment indicates toss starting at 2520 rpm of camshaft speed.

Computer Simulation of Dynamical Behavior of Self-Propelled Gurney

The conventional gurneys used in hospitals to move patients from room to room have one main disadvantage: they are difficult to control. A typical gurney has a form of an oblong table moving on four castor wheels. The vehicle is difficult to maneuver, especially on corridor turns, and usually requires two operators — each at one end. Dr. J. Bleicher from the St. Joseph’s Hospital in Omaha, Nebraska suggested a new type of a self-propelled gurney which would be a cross-breed of a motorized wheelchair and a gurney. A new type of a gurney would have two additional wheels in the center of the gurney, each connected to a separate DC motor. The torques developed by the motors would be controlled by one operator using a joystick. Applying opposite torques to the controlled wheels would rotate a stationary gurney in place, or would curve the path of a moving gurney. The position of two additional wheels can be changed, so that the gurney can move sideways, translate in chosen direction or move along a curvelinear path. The work presented in the paper contains an analysis of the dynamics of such a gurney. A mathematical model of the vehicle was developed to check how much effort is needed on the part of the operator in straight path motion and during negotiating a corner. The most difficult part of the modelling was a proper description of forces and torques exerted by the ground on the wheels. The differential equations of motion of the gurney have been numerically integrated, and the dynamical response of the vehicle studied. The results of the computer simulation show a transient oscillatory response of the castor wheels (shimmying) which can be controlled by a proper choice of design parameters of the vehicle.

Generation of Motion Equations for a Tree-Like System of Granular Bodies

An arbitrary system of 3D-bodies made out of rigid spheres and arranged topologically in a tree is considered. For such a system explicit expressions for the equations of motion are derived based on the Lagrangian approach. The equations are given in terms of the path matrix characterizing the topological tree. The analytical method of generation of equations of motion makes the computer simulation of the nonsteady motion of the discrete system of bodies more efficient in term of both computer time and accuracy. It is achieved by avoiding operations with large sparse matrices (if the equations were generated numerically) and by cancelling out some terms in Lagrange’s equations analytically.

A Comparison of Continuum and Lumped-Mass Models for Hyper-Redundant Manipulator Mechanics

The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator degrees-of-freedom. Furthermore, these methods are not fully parallelizable. For ‘hyper-redundant’ manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an ‘infinite degree-of-freedom’ (or continuum) problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.

Modeling and Optimization of Dissipative Properties of Industrial Articulated Manipulators

A mathematical model describing elastic and dissipative properties of manipulator links and joints is considered. An articulated manipulator is regarded as an open kinematic chain of absolutely rigid arms connected by flexible joints. Free and forced vibrations around goal manipulator configurations are studied. Friction forces are supposed to be applied to the manipulator hinges. They are described by the help of generalized dissipative function. According to this model the possibilities for damping the free and forced vibrations of industrial articulated manipulators are studied. Some problems for defining the optimal friction laws with regard to new energy criteria are solved. A global energy criterion depending on the total mechanical energy is proposed. It is proved that this functional doesn’t depend on the character of the transient oscillation process. A minimax problem is formulated and a computer oriented method for its solving is developed. Another energy criterion is connected with maximizing the average power dissipated for one period of forced oscillations. A general algorithm for defining the corresponding optimal periodic damp laws is worked out. The results obtained can be directly used for optimal passive and active damping of the vibrations of industrial manipulators by realizing of the corresponding friction laws.

Experimental Characterization of a Flexible Two-Link Manipulator Arm

Experiments were performed to verify the analytical models for a robotic manipulator with two flexible links. A finite element model (FEM) employing two-dimensional beam elements was used to model the structure. A proportional model relating input voltage to output torque was used for both hub and elbow joint motors. With some minor adjustments to the link stiffness, the FEM modal frequencies matched the experimentally extracted frequencies within 1.5%. However the voltage-torque relationship for the hub motor was found to exhibit dynamics in the frequency range of interest.

An Isoparametric Four-Node Beam Element for the Analysis of Planar Robot Manipulators

Accurate determination of the dynamic response of high speed flexible manipulators requires that the dynamic model incorporates the influence of joint compliances, in addition to faithfully representing the physical characteristics of the links. A finite element model is herein presented for this purpose. The model is based on a 4-node isoparametric Timoshenko beam element to model the structural characteristics of the links including the effects of shear deformation and rotary inertia. It also includes the influence of the rigid body motion and the time derivatives of the elastic deformations of the manipulator on the characteristic matrices of the system, and accounts for the inertia of the drive units and payload and the damping of externally applied dampers. Quasistatic analysis, modal analysis, and linear and nonlinear vibrational responses of a 3-R planar manipulator are determined by solving the appropriate equations of equilibrium. The results of the analysis revealed that the compliance of the joints have a considerable influence on the manipulator response which is manifested by considerable increase in endpoint deflections and substantial decrease in fundamental natural frequency. Nonlinear transient response exhibited a behavior that differs drastically from that obtained when rigid joints are assumed.