Laid down in this paper are the foundations on which the design of engineering systems, in the presence of an uncontrollable changing environment, can be based. The changes in environment conditions are accounted for by means of robustness. To this end, a theoretical framework as well as a general methodology for model-based robust design are proposed. Within this framework, all quantities involved in a design task are classified into three sets: the design variables (DV), grouped in vector x, which are to be assigned values as an outcome of the design task; the design-environment parameters (DEP), grouped in vector p, over which the designer has no control; and the performance functions (PF), grouped in vector f, representing the functional relations among performance, DV, and DEP. A distinction is made between global robust design and local robust design, this paper focusing on the latter. The robust design problem is formulated as the minimization of a norm of the covariance matrix of the variations in PF upon variations in the DEP, aka noise in the literature on robust design. Moreover, one pertinent concept is introduced: design isotropy. We show that isotropic designs lead to robustness, even in the absence of knowledge of the statistical properties of the variations of the DEP. To demonstrate our approach, a few examples are included.
In this paper, the design of a planar three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Four different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) the existence of a nonvanishing workspace for every orientation of the gripper (c) the maximization of the global workspace, and (d) the isotropy of the Jacobian of the manipulator. The four associated problems are formulated and their solutions are derived. Two of these require to resort to numerical methods for nonlinear algebraic systems. Results of optimum designs are also included.
In this paper, a novel bipod parallel grinder with four controlled degrees of freedom is introduced. The moving platform of this 2-leg parallel grinder can always keep moving in horizontal plane by means of four-parallelogram mechanism (Π joints). The closed-form solutions of forward and inverse kinematics are derived.
This thesis studies the estimation of the motion of a rigid-body from body-point motion data. This study is closely related to the direct kinematics problem in robotics, its solution being particularly challenging, at the displacement level, for parallel manipulators.
The concept of measurement subspaces is used to characterize the motion of the end-point of three-degree-of-freedom serial manipulators of general geometry for any joint-sensor layout. Once the motion of a redundant set of body points is characterized by its measurement subspaces, the pose estimation problem reduces to a linear least-square problem subject to the nonlinear constraint of proper orthogonality over the orientation variables. Although the solution of this problem requires a nonlinear numerical procedure, we proposed two alternative linear least-square estimates for its solution. The polar least-square estimate (PLS) is based on the polar decomposition of the unconstrained least-square solution, while the decoupled polar least-square estimate (DPLS) uses the same approach, but solves a decoupled version of the kinematic relationships. A decoupling equation is derived for general combinations of measurement subspaces, for which sufficient conditions for isotropic decoupling are proposed and illustrated with an industrial parallel manipulator. Isotropic decoupling is defined in this thesis. The computational cost and estimation accuracy of the proposed procedures are analysed through simulation and experimental studies. Some procedures exhibit fair estimation accuracy and low computational cost, and hence, are well suited for the purpose of on-line implementation.
A suitable formulation and the implementing algorithms for involute and octoidal bevel-gear generation are proposed in this paper. In particular, the exact spherical involute tooth profile of bevel gears and their crown-rack is obtained through the pure-rolling motion of a great circle of the fundamental sphere on the base cone. Moreover, the tooth flank surface of octoidal bevel gears is obtained as the envelope of the tooth flat flank of the octoidal crown-rack during the pure-rolling motion of its flat pitch curve on the pitch cone. The proposed algorithms have been implemented in Matlab; several examples are included to illustrate their applicability.
Visualization plays an important role in the design of new robots or work environments. Robot Visualization System for Windows (RVS4W) is an updated cross-platform version of its predecessor, the Robot Visualization System (RVS). RVS was developed at the Centre for Intelligent Machines, McGill University, in the 1990s. It was developed on IRIX, the UNIX dialect of Silicon Graphics Inc. (SGI). Since IRIX is native to SGI workstations, RVS does not run on Intel-based PCs. Therefore, the source code of RVS had to be modifled in order to use this tool on an Intel-based PC. Based on the two important attributes of RVS4W, i.e., open source and platform-independent, the proper development tools were chosen. RVS4W is an updated version of RVS. The user interface was rewritten from scratch. We have made an efiort to keep the user interface consistent and user-friendly. The existing kinematics engine was also debugged and improved. RVS4W incorporates many new features including routines to evaluate the characteristic length, maximum reach, optimum posture|for minimum condition number|and robot conditioning. This manual introduces the user to the window-driven environment of RVS4W. Acknowledgements
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