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.

Quadratic Time Increment Indexing for Stepper Motor Motion Control

A fundamental problem of mechanical motion control is that of indexing a mass reliably from one stationary position to another in a given time with as little power as possible. A quadratic time increment function is proposed and demonstrated for stepping motor control. With this function, a given motor can index a mass through a variety of index lengths. The indexing system includes a microprocessor to adjust the motor pulse timing to index the inertial load through a range of motions — each with the same maximum torque. The functions and the sizing of the motor are described. The interaction between the microprocessor calculation speed and the indexing capability is given for achievable real time control. Experimental results for a specific system are presented.

Design of Radial Cams With Zero Pressure Angle

The addition of an intermediate roller between the cam and the follower roller is proposed in this paper. The function of this intermediate roller is to reduce the pressure angle on the follower to zero. As a result of adding the proposed intermediate roller, all problems caused by the pressure angle in cam mechanisms are eliminated.