Balancing Conditions for Planar Mechanisms

One of the problems of the complete inertia force and moment balancing of planar mechanisms consists of the deriving from the so-called balancing conditions. In recent publications on this field these balancing conditions are seperately derived for each particular mechanism [1], [2], [3]. In the present paper a new method is presented which derives the balancing conditions for planar mechanisms with an arbitrary structure (except for mechanisms containing cam pairs) in generality. This algorithm is suitable for the application of computer algebra systems.

Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks

Approximate kinematic equations are developed for the analysis and design of three-input, eight-bar mechanisms driven by relatively small cranks. Application of a method in which an output link is presumed to be comprised of a mean and a perturbational motions, along with the vector loop approach facilitates the derivation of the approximate kinematic equations. The resulting constraint equations are, (i) in the form of a set of four nonlinear equations relating the mean link orientations, and (ii) a set of four linear equations in the unknown perturbations (output link motions). The latter set of equations is solved, symbolically, to obtain the output link motions. The approximate equations are shown to be effective in the synthesis of three-input, small-crank mechanisms.

A Symbolic-Numerical Approach for the Dynamic Modelling of Parallel Manipulators

A symbolic-numerical approach for the dynamic modelling of parallel manipulators is proposed in this paper. By extending the symbolic algebraic operation rules of the structural matrices and using an improved algorithm for the optimal operation of structural matrices, matrix elements in dynamic equations are generated automatically on the computer with minimization of number of floating-point multiplications/additions.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Mass Flow and Derivative Moment of Inertia Flow in Planar (Geared) Linkages

The paper describes a method for the determination of the conditions for the complete shaking force and shaking moment balancing of planar linkages, including geared linkages, with revolute and prismatic joints. The conditions may be written down without the need for any kinematic analysis of the linkage by the application of two new concepts. These are the concept of mass flow for complete shaking force balance and the concept of derivative moment of inertia flow for complete shaking moment balance, the second of which is described here for the first time. A number of examples demonstrate the power of the method.

An Optimal Design Method for Damping Structure With Constrained Viscoelastic Material

This paper describes an optimal design method for a damping structure using constrained viscoelastic material. The relationship between viscoelastic material behavior and the damping effect, is analyzed by finite element method, where viscoelastic material is modeled by discrete spring elements with the equivalent stiffness and loss factor. This finite element model is applied to the design of a head-gimbal-assembly (HGA) of a magnetic disk device and its reliability is confirmed experimentally. The analysis shows that the maximum deformation of the constrained viscoelastic material occurs at the edge area, so to optimize the damping structure, this area should be placed on the area of high strain energy. Although the damping effect by constrained viscoelastic material has been considered due to shear deformation of viscoelastic material, in this analysis, tensile deformation of the egde of viscoelastic material is strongly related to the damping effect for the bending and torsional modes of HGA. Therefore, an accurate analysis must consider tensile deformation of viscoelastic material.

Body Vibrations of a Legged Walking Machine

Unlike in wheeled vehicles, compliance in walking machine systems changes due to the variation of leg geometry, as its body proceeds. This variation in compliance will cause vibration, even if external loads remain constant. A theory is thus developed to predict the body vibrations of a walking machine during walking. On the other hand, dynamic foot forces under body vibrations can be computed by application of the existing numerical methods. As an example, the body vibrations of a quadrupedal walking chair under different walking conditions are simulated in terms of the developed theory. The results show that the influence of body vibrations on the foot force distribution is essential and, in some cases, the walking chair may lose its stability due to its body vibrations, even though it is identified to be stable in a quasi-static analysis. The developed theory can also be extended to other similar multi-limbed robotic systems, such as multi-fingered robot hands.

An Efficient Algorithm for Finding Optimum Code Under the Condition of Incident Degree

This paper deals with the identification of kinematic chains. A kinematic chain can be represented by a weighed graph. The identification of kinematic chains is thereby transformed into the isomorphism problem of graph. When a computer program has to detect isomorphism between two graphs, the first step is to set up the corresponding connectivity matrices for each graph, which are adjacency matrices when considering adjacent vertices and the weighed edges between them. Because these adjacency matrices are dependent of the initial labelling, one can not conclude that the graphs differ when these matrices differ. The isomorphism problem needs an algorithm which is independent of the initial labelling. This paper provides such an algorithm.

Kinematic Singularities of Free-Floating Open-Chain Planar Manipulators

This paper deals with Jacobian singularities of free-floating open-chain planar manipulators. The problem, in essence, is to find the joint angles where the Jacobian mapping between the end-effector rates and the joint rates is singular. In the absence of external forces and couples, for free-floating manipulators, the linear and angular momentum are conserved. This makes the singular configurations of free-floating manipulators different from structurally similar fixed-base manipulators. In order to illustrate this idea, we present a systematic method to obtain the singular solutions of a free-floating series-chain planar manipulator with revolute joints. We show that the singular configurations are solutions of simultaneous polynomial equations in the half-tangent of the joint variables. From the structure of these polynomial equations, we estimate the upper bound on the number of singularities of free-floating planar manipulators and compare these with analogous results for structurally similar fixed-base manipulators.