Determination of the Workspace of 6-DOF Parallel Manipulators

This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

Dynamic Calibration for Serial Robotic Manipulators Based on the Zero Position Analysis Method

In the continuation of a kinematic calibration method developed in a previous report, a new dynamic calibration model for serial robotic manipulators is presented in this paper. This model is based on the Zero Position Analysis Method. It entails the process of estimating the errors in the robot’s dynamic parameters by assuming that the kinematic parameters are free of errors. The convergence and effectiveness of the model are demonstrated through numerical simulations.

Object Oriented Dexterity Analysis and Design Application for Spatial Robot Hands

For an arbitrarily shaped object manipulated by a robot hand, this paper presents a procedure for analyzing the position and rotation ranges of the object, and a procedure for designing the kinematic parameters of a hand to meet given requirements on the motion ranges. Rotation dexterity index, dexterity charts, and a dexterity scalar characterizing both position range and rotation range are introduced for the performance evaluation of a robot hand. Least-square-error iteration and steps are detailed for the kinematic parameter determination of a robot hand.

Synthesis of Geometric Primary Circles of Externally Meshed Skew-Axes Gears

What are considered are geometric primary circles of gears which transform rotations between fixed skewed axes with a constant speed ratio. These imaginary circles differ from the pitch ones of the gears with parallel or intersecting axes. It seems they are used succeessfully for the first time as a start point in designing hyperbolic gears. Both the diameters and the mutual position parameters of the geometric primary circles are needed when gear over-alls and mounting distances as well as teeth geometry are determined.

Applications of Symbolic Computing for Numerical Analysis of Mechanical Systems

The symbolic computing system MACSYMA is used to automatically generate the explicit equations necessary to represent the kinematic constraints and system dynamics and to compute the design sensitivities for optimal design of any multibody system. The logic to construct system matrices and vectors involved in the analysis and design equations is implemented as general purpose MACSYMA programs. All necessary manipulations are performed by MACSYMA and the equations are output as FORTRAN statements that can be compiled and executed. This approach results in a computational saving of up to 95% compared to using a general purpose programs. The approach is general in nature and is applicable to any multibody system. Examples are presented to demonstrate the effectiveness of the approach.

Modeling, Simulation, and Modal Analysis Hydraulic Valve Lifter With Oil Compressibility Effects

A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multi-mode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid In the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, non-linear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.

Comparative Performance of Isotropic and Composite Bladed Disks

Using a 3-noded, multilayered anisotropic triangular plate and shell element combined with cyclic symmetry method, a comparison has been drawn on the steady state as well as free vibration behaviour of isotropic and composite bladed disks, taking into account all the geometric and material complexities. Results are presented for a representative model for three cases – isotropic bladed disk, isotropic disk-composite blade, and composite bladed disk.

Optimization of Dynamic Forces in the Design of Mechanical Hands

Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.

Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops

This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

Hydrodynamic Lubrication of Pocket Bearings and Effect of Contouring the Inner and Outer Regions, and Optimum Design Data

The article investigates pocket bearings with contoured profiles of exponential forms on both surfaces inside and outside of the step boundary forming hydro-dynamic action surfaces, and develops optimum design data yielding efficient slider bearings with small pockets with higher load capacities than conventional pocket bearings. In the case of a pocket bearings, in addition to the Reynolds equation used for the regions inside and outside the pocket, the continuity equation along the pocket boundary is satisfied to form the complete model of the bearing. The optimum design data includes dimensionless load-, flow-, temperature rise-, power loss-, stiffness-, and the coefficient of friction factors. Incompressible lubricant with temperature dependent viscosity is considered. Detailed study of conventional pocket bearings with planar surfaces is included. Some optimum exponential pocket bearings yield up to 561 percent increase in load capacity as compared to the conventional tapered bearings.