Open-loop Mechanisms Research Articles

Characteristic Evaluation and Comparisons of Robotic Mechanisms. 1st Report, Evaluation and Comparisons Based on Static Characteristics.

This paper compared and evaluated several kinds of representative robotic mechanisms based on static characteristics. In particular, open-loop mechanisms and two kinds of closed-loop mechanisms, that is, parallel crank mechanisms, were adopted as the representative robotic mechanisms. On the characteristic comparisons of the robotic mechanisms, former research had been carried out on the condition that the configurations of the mechanisms were limited to a certain form. However, static characteristics of the robots are greatly changed by the mechanism configurations. Therefore, this paper paid special attention to the changes of each mechanism characterized by those configurations. Geometrical characteristics, strength characteristics and characteristics based on input/output displacement of these robotic mechanisms were compared and evaluated. As a result, the superior and inferior characteristics of each robotic mechanism were revealed.

モータ代数とグラフ理論による機構の記述と解析 (第3報)

Equation of motion of an open loop mechanism is formulated by describing the equilibrium of external force and inertia force around each pair-axis. The topology of an open loop mechanism is represented by a tree-path matrix having the stationary link as its root. An inertia force motor on a link is determined by the extended tensor of inertia in 6 × 6 matrix form, the velocity motor and the acceleration motor of the link. The equation of motion is interpreted in two ways. Firstly, it can be used to calculate the driving torque of each pair axis to realize the specified motion of an open loop mechanism. Secondly, relative angular acceleration at each pair is determined through the equation by velocity motors and external forces of all links. A computer program based on the new equation is developed for three-dimensional dynamic analysis of open loop mechanisms. When the initial state of an open loop mechanism and the external force functions are given, the motion of the mechanism can easily be simulated by numerical integration. Application to some typical motion analysis problems proved the effectiveness of the program.

An inverse kinematic analysis procedure for flexible open-loop mechanisms

This paper presents the development of a point-oriented kinematic analysis procedure for open-loop mechanisms that includes provision for elastic links. The analysis method is based upon specifying the three-dimensional reference locations of control points that lie at specified locations on the mechanism. An iterative method based upon 4 × 4 transformation matrix techniques is utilized to solve for the values of the joint variables that define the configuration of the mechanism as well as their velocities and accelerations. This is first done with the assumption that the mechanism links are rigid in order to determine the nominal mechanism state for load calculation purposes. Quasi-static loading conditions are assumed in order to calculate the deformed shapes of the links which are then used to reiterate on the position analysis. The method incorporates least-squares to allow the solution when the control point data is underspecified, overspecified or inconsistently specified. Examples are provided in which the analysis procedure incorporating elastic links is applied to the solution of two planar manipulator positioning problems.

A finite element model for the dynamics of flexible manipulators

An analytical method based on a Lagrangian formulation is presented to modelize the dynamics of spatial, multi-link, open-loop mechanisms such as manipulators. A finite element model is used to study the structural behaviour of the links, using the displacements referenced in the rigid body motion configuration as degrees of freedom. The finite element model is combined with the 4 × 4 matrix dynamics formulation and the equations of motion are derived from the Lagrangian of the system. They are solved using a two parameters single step algorithm which has proved to be efficient. Examples using a 2D beam element are presented.

A new vector theory for the analysis of spatial mechanisms

This paper develops a new vector theory for the analysis of spatial mechanisms on the basis of the vector analysis theory and dual-number algebra and the recursive notation presented by J. Duffy. The new vector theory includes the displacement, velocity and acceleration equations for the open kinematic chains and loop mechanisms. The displacement equations for the loop mechanisms are classified into four groups with two forms, namely the primary, secondary, projective and the fourth-group loop/half-angle equations, which have been applied to the derivation of the 16th degree polynomial input-output equations in the tan-half-angle of the output angular displacements for the general spatial 7-link 7R and 6R-P mechanisms, etc. In the analysis of the velocity and acceleration, the differential calculus are changed into vectorical algebraic operations and the unified equations are expressed in the vector forms which are linear in the velocity and acceleration variables.

Interactive Modeling and Analysis of Open or Closed Loop Dynamic Systems with Redundant Actuators

This paper deals with the development of a computer-based procedure for the modeling and analysis of large displacement dynamic systems of the open or closed loop types. The procedure facilitates the construction of the model for such systems, automatically formulates the dynamic equations and provides the solution for any given input motion. The program is capable of analyzing complex systems with redundant force actuators utilizing a linear programming optimization scheme. It incorporates an interactive graphic capability which is invaluable in the construction, modification and visual checking of a model. The modeling procedure is general in nature and is applicable to systems of many connected rigid bodies. Its capabilities are illustrated in this paper by evaluating muscle forces and joint reactions of the musculoskeletal structure during dynamic activity. The system is readily applicable to the analysis of the actuation schemes in human and animal locomotion, many classes of machine systems, as well as robots and manipulators. Although only applications to open loop mechanisms are presented in this paper, the program can be readily extended to treat closed loop systems as well.