Trajectory Synthesis and Redundancy Resolution for High Speed Point to Point Motions of Redundant Robot Manipulators

Trajectory synthesis for robot manipulators with redundant kinematic degrees-of-freedom has been studied by numerous investigators. Redundant manipulators are of interest since the redundant degrees-of-freedom can be used to improve the local and global kinematic and dynamic performance of a system. As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Noting that manipulators with revolute joints have nonlinear dynamics, high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. In this paper, a redundancy resolution method is developed based on the Trajectory Pattern Method (TPM) to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. As an example, optimal trajectories are synthesized for point to point motions of a plane 3R manipulator.

Synthesis of a Large Oscillation Four-Bar Mechanism

This paper demonstrates procedures implemented for the synthesis of a four-bar mechanism that produces large angular oscillations of the output member while maintaining effective transmission angles. The mechanisms are modeled as being driven by a force applied at the coupler link. Additionally this force’s line of action is constrained to occur along an approximate straight line. This research was conducted out of the need for a device that is capable of retraction of the horizontal tool bar housed on the back of a tractor. The tool bars accommodate the implements required to accomplish the numerous tasks of the farmer, i.e. row markers, sprayer arms, planters, etc. Upon retraction of the tool bar so that it is parallel to ground, the appropriate tools are lowered to their working position. As the length of these bars increases, a savings of time and increased productivity is realized. Kurt Hain makes the following observation regarding large oscillation mechanisms in [1]: “It would be very difficult to solve this problem with one four-bar linkage, because it is difficult to design a four-bar linkage having such a large oscillation of a crank without running into problems of poor transmission angle characteristics; it might be possible to use linkages in combinations with gears, but this would make the mechanism more expensive, less efficient, and probably noisier.” In this study simulated annealing, a genetic algorithm and the generalized reduced gradient method are used to produce mechanisms with large angular oscillations of the output member and transmission angles that vary by as little as 20° from 90°. A comparative analysis of each of the optimization procedures is presented with observations regarding the efficacy of each method in the solution of the large oscillation mechanism.

The Problem of Size in Robust Design

To facilitate the effective solution of multidisciplinary, multiobjective complex design problems, a departure from the traditional parametric design analysis and single objective optimization approaches is necessary in the preliminary stages of design. A necessary tradeoff becomes one of efficiency vs. accuracy as approximate models are sought to allow fast analysis and effective exploration of a preliminary design space. In this paper we apply a general robust design approach for efficient and comprehensive preliminary design to a large complex system: a high speed civil transport (HSCT) aircraft. Specifically, we investigate the HSCT wing configuration design, incorporating life cycle economic uncertainties to identify economically robust solutions. The approach is built on the foundation of statistical experimentation and modeling techniques and robust design principles, and is specialized through incorporation of the compromise Decision Support Problem for multiobjective design. For large problems however, as in the HSCT example, this robust design approach developed for efficient and comprehensive design breaks down with the problem of size — combinatorial explosion in experimentation and model building with number of variables — and both efficiency and accuracy are sacrificed. Our focus in this paper is on identifying and discussing the implications and open issues associated with the problem of size for the preliminary design of large complex systems.

Dynamic Modelling of a Three Degree-of-Freedom Planar Platform-Type Manipulator

In this paper, the dynamic modelling of a planar three degree-of-freedom platform-type manipulator is presented. A kinematic analysis is carried out initially to evaluate the initial coordinates and velocities. The dynamic model of the manipulator is formulated using a two-step transformation. Initially, the dynamic formulation is written in terms of the Cartesian coordinates of a dynamically equivalent system of particles. Since there is no rotational motion associated with a particle, then the differential equations of motion are derived by applying Newton’s second law to study the translational motion of the particles. The constraint forces between the particles are expressed in terms of Lagrange multipliers. Then, the differential equations of motion are written in terms of the relative joint variables. This leads to an efficient solution and integration of the equations of motion. A numerical example is presented and a computer program is developed.

Utilizing the Effort/Motion Approach in the Simulation of Interconnected Rigid Body Systems

The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

Multiobjective Collaborative Optimization

This investigation focuses on the development of modifications to the Collaborative Optimization (CO) approach to multidisciplinary systems design, that will provide solution capabilities for multiobjective problems. The primary goal of this research is to provide a comprehensive overview and development of mathematically rigorous optimization strategies for MultiObjective Collaborative Optimization (MOCO). Collaborative Optimization strategies provide design optimization capabilities to discipline designers within a multidisciplinary design environment. To date these CO strategies have primarily been applied to system design problems which have a single objective function. Recent investigations involving multidisciplinary design simulators have reported success in applying CO to multiobjective system design problems. In this research three MultiObjective Collaborative Optimization (MOCO) strategies are developed, reviewed and implemented in a comparative study. The goal of this effort is to provide an in depth comparison of different MOCO strategies available to system designers. Each of the three strategies makes use of parameter sensitivities within multilevel solution strategies. In implementation studies, each of the three MOCO strategies is effective in solving two multiobjective multidisciplinary systems design problems. Results indicate that these MOCO strategies require an accurate estimation of parameter sensitivities for successful implementation. In each of the three MOCO strategies these parameter sensitivities are obtained using post-optimality analysis techniques.

Dynamics Modeling of Elastic Multibody Systems Using Kane’s Method As Applied to a Flexible Robot

Generalization of Kane’s equations of motion for elastic multibody systems is considered. Initially, finite element techniques are used to generate the elastic form of generalized coordinates. Then, the number of elastic coordinates are reduced by the component mode synthesis. Finally, Kane’s method is applied to obtain the equations of motion of such systems. Using this method, dynamic model of an elastic robot with one degree of freedom is presented.

Thermal Issues in the Design of an SLS Rapid Prototyping Machine

In Selective Laser Sintering (SLS), one of several powder-based Rapid Prototyping (RP) methods, thermal transfer plays an important role in machine design. Thermal control of the processing area or “space” is crucial for accurate, repeatable part formation. In a typical SLS powder bed, significant thermal transfer occurs through mixed convection and conduction. In this paper, a polymeric powder bed subjected to in-bed convection is investigated with the goal of quantitatively determining transient thermal behavior. A numerical model describing heat transfer within a powder is presented. Convection and conduction are both numerically shown to play important roles in steady state temperature profiles. The design and construction of an experimental apparatus to measure the temperature profiles within a powder subjected to forced convection are also described. Full factorial experiments are used to calibrate and validate the numerical model, as well as to examine transient behavior. Using information gained from numerical and experimental work, suggestions are made for machine design to better control part precision and reproducibility. For example, it is shown that actively controlling the temperature of air convected through the powder bed gives fine, rapid control over the feed side cylinder thermal state.

Synthesis of Distributed Compliant Mechanisms for Adaptive Structures Application: An Elasto-Kinematic Approach

Compliant mechanisms are a class of mechanisms that achieve desired force and motion transmission tasks by undergoing elastic deformations as opposed to rigid-body displacements in the conventional rigid-link mechanisms. Most of the previously reported synthesis studies in compliant mechanisms related to either partially-compliant mechanisms or fully-compliant mechanisms with joint compliance. Methods developed for fully-compliant mechanisms with link compliance addressed the issue of topology generation for desired deflections at discrete points on the mechanism. This paper presents a new, first-principles based synthesis procedure for fully-compliant mechanisms with link compliance — that is, distributed-compliant mechanisms — for continuous shape change requirements in a particular segment of a mechanism. The general approach presented in this paper for the synthesis of distributed compliant mechanisms is shown to be well suited for application in the design of adaptive structures, an emerging class of high-performance structural systems. The current trend in the design of adaptive structures is to embed structures with force or strain inducing “smart” materials to serve as distributed actuators. Potential advantages of using the distributed compliance scheme over the distributed actuation scheme in the design of adaptive structures include a significant reduction in the number of required actuators and controls.

Formation of Geometric Tolerance Zones for Polyhedral Objects

This paper presents a scheme for establishing geometric tolerance zones for polyhedral objects in solid modelers. The proposed scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface’s model variables. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specifications. Appropriate algebraic constraints (on the model variables) are finally used to establish the tolerance zone boundaries in the surface-based variational model.