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EDITORIAL

J. Mech., Trans., and Automation. 1988;110(1):1. doi:10.1115/1.3258898.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Mechanisms Papers

J. Mech., Trans., and Automation. 1988;110(1):3-10. doi:10.1115/1.3258902.

A method is presented for calibration of a robot to correct position and orientation errors due to manufacturing. The method is based on the shape matrix robot kinematic description. Each joint is individually and successively moved in order to explicitly calculate the shape matrix of each link. In addition, methods to correct for the errors in both the forward and inverse kinematic solutions are presented. The modification of the forward solution is a simple task. The modification of the inverse kinematic solution is a difficult problem and is achieved by an iterative technique which supplements the closed-form solution. An example of the calibration and inverse solution is presented to show the improvement in the accuracy of the robot.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):11-15. doi:10.1115/1.3258896.

In this article, disc cams with translating followers are studied and the speed fluctuation of the input shaft is minimized with respect to eccentricity. First, the equations of motion for the cam mechanisms with roller follower and flat-faced follower are determined. Then, by solving these equations for steady-state motion, the coefficient of speed fluctuation is calculated. The optimum eccentricity that would minimize the coefficient of speed fluctuation is determined.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):16-21. doi:10.1115/1.3258897.

This paper deals with the first and higher-order function-generation problems in the synthesis of linkages with relatively small input cranks. Such linkages tend to produce nearly simple harmonic motions at the output members. Owing to this distinction, the generality of the conventional synthesis techniques is no longer applicable. Thus, in function generation, only harmonic functions of the input motion may be expected to be synthesized for output motions.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):22-27. doi:10.1115/1.3258899.

This paper, a sequel to a companion paper on function generation, discusses the path and motion generation problems in the synthesis of linkages with relatively small input cranks. The point on the floating link (i.e., the coupler of a crank-rocker linkage or the connecting rod in a slider-crank linkage) traces an approximate ellipse. This fact serves as a major distinction between the method described herein and the conventional, more general, synthesis techniques. In other words, only elliptical paths may be generated by the path (or coupler) points in the synthesis of linkages with small cranks. Higher-order path and motion generation, in which velocity, acceleration, slope and the rate of change of slope of the coupler path may be specified, are also addressed in this paper.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):28-34. doi:10.1115/1.3258900.

A method for the dynamic analysis of flexible legged locomotion systems that accounts for the rotary inertia and shear deformation effects is presented. The motion of the flexible components in the legged vehicle is described using a set of inertia-variant Timoshenko beams that undergo large rotations. A shape function that accounts for the combined effect of rotary inertia and shear is employed to describe the deformation relative to a selected component reference and the rigid-body modes of the shape function are eliminated using a set of reference conditions. Kinetic and strain energies are derived for each Timoshenko beam, thus identifying the beam mass and stiffness matrices which account for the rotary inertia and shear deformation effects. A new set of time-invariant matrices that describe the nonlinear inertia coupling between the reference motion and elastic deformation and account for the rotary inertia and shear is developed and it is shown that the form of these matrices as well as the mass and stiffness matrices are significantly affected by the inclusion of rotary inertia and shear. Numerical experimentations indicate that shear and rotary inertia can have a significant effect on the dynamics of flexible legged locomotion.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):35-41. doi:10.1115/1.3258901.

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.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):42-47. doi:10.1115/1.3258903.

For 4R manipulators and their various possible configurations, workspaces with full, partial, and zero dexterity are defined, and a procedure to determine them is developed. As examples, two 4R manipulators are analyzed. Subspaces with 2, 4, 6, and 8 configurations and various degrees of dexterity are found. Several points on the effect of geometrical parameters on the shape and extent of the boundary surfaces, subspaces, and number of configurations are discussed. An index for the evaluation of the degree of accessibility of the workspace of a manipulator is also proposed.

Topics: Manipulators , Shapes
Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):48-55. doi:10.1115/1.3258904.

This investigation is concerned with the thermoelastic analysis of flexible multibody machine-tool mechanisms using the finite-element method. Thermoelastic response of the machine tool is obtained by discretizing the machine tool into a number of simple elements and calculating the thermal stress and strain of each element under the average temperature rise. The generalized thermoelastic forces associated with the generalized elastic coordinates are then determined using the virtual work. The nonlinear dynamic behavior of the machine-tool mechanism due to the application of a constant cutting force as well as a chattering (dynamic) force, with and without thermal effects, is analyzed. The chattering force is obtained by considering the cutting force variations due to the variation of undeformed chip thickness and the rate of penetration of the tool, as a result of tool deformation. In this investigation, the machine-tool mechanism is considered as a multibody system consisting of interconnected rigid and flexible bodies that undergo large angular rotations. Bending and axial deformation of the elastic bodies in the system are considered. Component mode synthesis techniques are employed in order to reduce the number of elastic coordinates and the system differential equations of motion and nonlinear algebraic constraint equations are written in terms of a coupled set of reference and modal elastic coordinates. The formulation is exemplified using a crank-shaper mechanism wherein the flexibility of the tool as well as the flexibility of the mechanism links are considered.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Design Automation Papers

J. Mech., Trans., and Automation. 1988;110(1):58-64. doi:10.1115/1.3258907.

A new algorithm for linear programming problems is presented. The algorithm makes interior moves with a special active set strategy that utilizes both local and global knowledge. This knowledge represents primarily monotonicity and dominance information. The article describes the rationale, theory, implementation, and some test examples for the algorithm. The ideas presented form the basis for nonlinear programming extensions in sequel articles.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):65-72. doi:10.1115/1.3258908.

A design technique is presented which modifies system dynamics by simultaneously considering control system gains and structural design parameters. Constraint functions are devised that become smaller as (1) structural design parameters and feedback gains become smaller, and (2) closed-loop eigenvalues migrate toward more desirable regions. By minimizing a weighted sum of these functions, the interaction between design performance and design parameters can be explored. Examples are given that show the effects of the weighting parameters, and the potential advantages of this technique over traditional pole placement techniques.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):73-80. doi:10.1115/1.3258909.

An important step within the automated type synthesis process is the generation of graphical displays of proposed mechanisms which permit designers to visualize the candidates. In this paper, the concepts of kinematic icon and inactive joint have been developed and applied to the problem of automatically generating sketches of mechanisms, given only the kinematic structure. Each different link type is treated as a separate entity: an icon, with its own predefined graphical representation. Moving-link icons, (as opposed to icons of fixed links) have special properties defined according to the joint types on the adjacent links. The locations, sizes, and orientations of the icons depend on the locations of the joints whose coordintaes may be directly assigned (in simple cases) using joint placement procedures. However, because the icons are defined by assigning a specific graphical representation to groupings of joints, and not just single joint, not all joints can be directly assigned their coordinates and this other class of kinematic joint is defined as an inactive joint. The kinematic icon and inactive joint concepts make possible the sketching of mechanisms with more complicated joint types such as prismatics and gears, for the first time in a systematic manner.

Topics: Mechanisms , Gears
Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):81-87. doi:10.1115/1.3258910.

Monotonicity analysis is used to solve a three-objective optimization problem in which a hydraulic cylinder is to be designed. With the additional application of the Karush-Kuhn-Tucker optimality conditions a reduced symbolic design chart is obtained which is then utilized to obtain parametric numerical results. Two- and three-dimensional parametric Pareto-optimal plots are obtained for the three conflicting objectives: (1) cross-sectional area, (2) circumferential stress ratio and (3) pressure ratio. The analysis and design procedure strengthens and extends the results suggested by previous works.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):88-92. doi:10.1115/1.3258911.

The tri-level variable rate trajectory is a general motion which can be applied to programmable controllers, robotic manipulators, mechanisms, and mechanical devices where the input crank orientation, velocity, and acceleration vary with time. In the work presented here, the tri-level variable rate trajectory is an extension of the variable-rate trans-symmetric motion developed by the first author in 1984. That motion and the one developed here consist of discrete segments of constant and linearly varying accelerations occurring over specified time intervals, thereby providing versatile programmable trajectories with several advantages over the constant acceleration motion, simple harmonic motion, cycloidal motion, and the popular polynomial trajectories used in robotics. The tri-level variable-rate trajectory allows much more control of the acceleration contour of the motion and as a result, there is a decrease in the power required, a decrease in the operating cost, and a decrease in dynamic responses such as shock, vibration, and shaking force and virtual elimination of the overshoot problem that sometimes accompanies the polynomial segment motions. This is a general method which can be applied to many applications. The results of applying this trajectory to a complex machine controller are presented as an example.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Power Transmission and Gearing Papers

J. Mech., Trans., and Automation. 1988;110(1):93-99. doi:10.1115/1.3258912.

The normal and tangential belt forces for two types of flat belts are measured and compared. From friction theory, it was assumed that the actual contact area A a is proportional to normal pressure p ; i.e., A a αp n . For a flat belt with cloth backing, the n =2/3 is obtained for the belt surface contact model. For a flat belt with rubber backing, which is used for power transmission, the n = 0.9 to 1.0 is suggested as a surface model. Different friction surfaces, construction materials, and geometries for the two belts resulted in different contact patterns and different friction characteristics.

Commentary by Dr. Valentin Fuster
J. Mech., Trans., and Automation. 1988;110(1):100-104. doi:10.1115/1.3258894.

Though the dynamic loads on gear teeth have been investigated for more than half a century, there is, so far, still a need to develop a general analytical theory, which can take into account the effect of the tangential location change of the conjugate contact point due to profile error and elastic deformation on the dynamic loads. In this paper, such a theory, which applies not only the theory of dynamics and the theory of elasticity but also the theory of conjugate surfaces [1, 2, 3] to solve the problem, and which is hence called Conjugato-Elasto-Dynamics, or simply CED, is developed and briefly sketched. Equations for determination of the dynamic loads on gear teeth are derived, which can be solved numerically by an iterative method with the aid of computer and the finite element method (FEM).

Commentary by Dr. Valentin Fuster

DISCUSSIONS

BOOK REVIEWS

J. Mech., Trans., and Automation. 1988;110(1):105-106. doi:10.1115/1.3258895.
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Abstract
Topics: Gears , Geometry
Commentary by Dr. Valentin Fuster

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