Synthesis and Balancing of Cam-Modulated Linkages

Linkages are inherently light, inexpensive, strong, adaptable to high speeds and have little friction. Moreover the class of functions suitable for linkage representation is large. For all these reasons numerous recent works deal with the problem of design mechanisms for robotic applications, but very often in terms of components such as gripper, transmission, balancing. We investigate a new application for linkages, using them to design industrial manipulator. The selected mechanism for this application is a four bar linkage with an adjustable lengh for exact path generation. This adjustment is performed by a track or cam which is substituted to a bar. By this mean, we define a cam-modulated linkage which possess superior accuracy potential and is capable of accomodating of industrial design restrictions. Such a kinematic chain is free from structural error for path generation and the presence of the track introduces the flexibility and versality in the usefull four bar chain. The synthesis technique of cam modulated linkage utilizes loop closure equations, envelop theory to find the centerline and the profile of the track. These techniques provide a systematic approach to the design of mechanism for path generation when extreme accuracy is required. In order to complete an contribution, we take in consideration the static balancing of the synthesized manipulator. To achieve static mass balancing we use the potential energy storage capabilities of linear springs, and integrated it with the non-linear motion of mechanism to provide an exact value of the desired counter loading functions. Examples are worked to demonstrate applications of these procedures and to illustrate the industrial potential of spring balancing and cam-modulated linkage.

Cam Motion Synthesis Using Spline Functions: Part I — Basic Theory and Elementary Applications

The application of spline functions to the general synthesis of cam motion programs is presented. The approach provides a single, systematic, easily automated method of accommodating discrete constraints on follower displacements, velocities, and accelerations, even when the set of constraints becomes large. It also allows the designer to develop refined motion characteristics while still satisfying the discrete constraints. A series of examples is presented to illustrate application of the method and to compare it to the more traditional techniques.

Hypotrochoidal Versus Epitrochoidal Gerotor Type Pumps With Special Attention to Volume Change Ratio and Size

The planar rotary mechanism, by virtue of its volume changing ability can be used as a pump, engine or compressor. Most of the types of rotary mechanisms used today, from the Wankel rotary engine to the gerotor pump, are based on epitrochoidal generation and its conjugate shape. This paper presents the mathematical relationships for the hypotrochoidal generation and also compares the flow rate, pocket and pump displacement between the hypotrochoidal and epitrochoidal generated profiles.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

Dynamic Modeling of a Multi-Legged Robotic Vehicle: Part 2 — Dynamic Analysis

In Part 1 of this report, we described the overall objective of the investigation; that is, the formulation of a dynamic model for determining the time response of a multi-legged robotic vehicle traveling on a variable-topographic terrain. Specifically, we developed expressions for the joint variables, and their rates, which are essential for describing the system’s links orientations, velocities, and accelerations. This procedure enabled us to determine the kinematic quantities associated with the entire vehicular system in accordance with the Newton-Euler method. In the present paper, we formulate the kinetic equations for the multi-degree-of-freedom leg assemblies, the rigid wheels, and the platform of the vehicle to achieve the prescribed motion and corresponding configuration of the system.

The Image of the Coupler Motion of a Special Spherical Four Bar Linkage

This paper uses a kinematic mapping of spherical motion to derive an image curve which represents the coupler motion of a doubly folding spherical four bar linkage. The image curve of this linkage, the so called “kite” linkage, can be parameterized by rational functions. This parameterization is presented as well as formulas which allow the computation of its curvature and torsion at any point. These formulas provide a link between the global properties of the coupler motion as represented by the image curve itself and its instantaneous properties given by the curvature and torsion functions.

Kinematic Displacement Analysis of a Double-Cardan-Joint Driveline

The input-output displacement relations of two Cardan joints arranged in series on a driveline has been investigated in detail, including the effects of unequal joints angles, the phase angle between the two Cardan joints and also such manufacturing tolerance errors as non-rigth angle link lengths and offset joint axes. A combined Newton-Raphson and Davidson-Fletcher-Powell optimization algorithm using dual-number coordinate-transformation matrices was employed to perform the analysis. An experiment was conducted to validate the results of the analysis. The apparatus consisted of a double-Cardan-joint driveline whose rotations were measured by optical shaft encoders that were sampled by a computer data-acquisition system. The equipment was arranged so that the phase angle between the joints and the offset angles between the shafts at each of the two joints could be readily varied. The “relative phase angle”, the difference between the phase angle of the two joints and the angle between the planes defined by the input and intermediate and the intermediate and output shafts, was found to be the significant factor. If the offset angles at both Cardan joints are equal, the double-Cardan-joint driveline function as a constant-velocity coupling when the magnitude of the relative phase angle is zero. If the offset angles at the two Cardan joints are unequal, a condition prevailing in the important front-wheel-drive automobile steering column, then fluctuation in output velocity for a constant input velocity is minimized although not eliminated for zero relative phase angle.

Primary Workspace of Simple Six-Link Robots

This paper presents an analytical study on the primary workspace of some simple six-link robots. The approach is to divide the structure of a six-link robot into two subsystems, the regional structure and the wrist. Taking advantage of the kinematic simplicity of three-link subsystems, we at the same time are able to solve the problem of reassemblage of the subsystems by using the concept of vector fields at the connection. Two types of wrist, the Euler Angle wrist and the Roll-Pitch-Yaw wrist are considered. (For Roll-Pitch-Yaw wrist, only Cartesian and articulated regional structures are included). Criteria for these robots to access points from specific directions are firstly developed. The theorems regarding accessing points from all directions are then derived. Finally clean statements on the boundaries of primary workspace are made.

Reliability Analysis of Robot Manipulators

A probabilistic approach to robot kinematics is presented and the concept of manipulator reliability is introduced to obtain a better evaluation of the performance of manipulators. Techniques are presented to compute this reliability and its relationship to the geometric parameters such as tolerances and arm configuration are discussed. The aspects of accuracy and repeatability of manipulators are explained in terms of manipulator reliability. The reliability of a two-link planar manipulator and the Stanford arm are considered for numerical illustration.

On the Derivation of Grashof-Type Moveability Conditions With Transmission Angle Control for Spatial Mechanisms

Derivation of Grashof-type conditions for spatial mechanisms that may include transmission angle limitations are discussed. It is shown that in general, different conditions need to be derived for each one of the existing configurations of the mechanism. In the absence of any transmission angle control, the conditions would be identical for pairs of configurations. As an example, for RRRSR mechanisms, Grashof-type conditions that ensure crank rotatability, the existence of a drag link type of mechanism, single or multiple changeover points, the possibility of full rotation at intermediate revolute joints, etc., are determined. A general discussion of the problems involved in such derivations, the use of approximation techniques to overcome some of the problems, and several other related subjects are presented.