This paper presents an extremely fast and reliable sensor-based algorithm that utilizes a combination of optimization techniques and heuristics to accomplish obstacle avoidance and path planning of mobile robots in real-time. This algorithm assumes no previous knowledge of the workspace and is capable of dealing with arbitrarily shaped obstacles with arbitrary motion characteristics. The concept of feasible circle is introduced to determine an obstacle-free subspace around the robot using information which can be obtained from distance sensors. This algorithm employs a unified approach and the modified Lagrange Multiplier method of optimization. A variable penalty, based on the distance of approach is used to keep the robot away from obstacles and the concepts of artificial obstacles and virtual obstacles are introduced to simplify the representation of the known workspace and to control the path of the robot. It is shown that the algorithm is general and can handle concave obstacles, overlapping obstacles, crowded workspaces as well as convex obstacles. The flexibility of the algorithm enables it to be easily integrated with different control strategies. The computational complexity is considerably less than for many existing algorithms, which makes the algorithm attractive for real-time applications. The algorithm is further extended to dynamic obstacles of arbitrary shapes and motion characteristics. Several case studies are presented to illustrate the capabilities of the algorithm.

The closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, the use of mobility charts is used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. The determination of the transmission angle for the RSCR mechanism is also described and numerical examples for function, path and motion generation are also included. This new closed form method of analysis based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.

The general procedure for synthesizing the rack and pinion mechanism for six precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for generating both four prescribed path points with input coordination and two positions of function generation. This is the extension of the work reported earlier on this mechanism where only three path precision points were satisfied. The rack and pinion mechanism has a number of advantages over the conventional four bar linkage mechanism. First, since the rack is always tangent to the pinion, the transmission angle has a constant optimum value of 90 degrees minus the pressure angle of the pinion. Second, because both translation and rotation of the rack are possible, multiple outputs are available. Generation of monotonic functions for a wide variety of motion, and nonmonotonic functions for the full range of motion as well as nonlinear motions, are other advantages of this mechanism. The rack and pinion mechanism has applications in the packaging industry, in toys, and automotive steering mechanisms. In this work, the mechanism is made to satisfy a number of practical design constraints such as a completely rotatable input crank and others. Also, structural errors for function generation are calculated to give an estimate of the accuracy of the mechanism. The method of solution developed in this work uses the complex number method of mechanism synthesis and a FORTRAN program is written to find the solutions for any input.

The Variable Geometry Truss Manipulator (VGTM) is a truss structure composed of tetrahedron elements stacked upon each other. Although this manipulator is geometrically different from a serial link manipulator, it is kinematically equivalent to the serial link manipulator whereby the difference in construction lies in its 120° twist angles instead of the more common 0° or 90°. A study of the dynamic behavior of a manipulator is important for simulation of the motion of the manipulator, designing suitable control equations and for evaluating the kinematic design and structure of the manipulator. In this paper the dynamic equations of motion have been derived for the VGTM. The different components of the torques have been computed using the Lagrange-Euler equations with the intention of studying the contributions of each term. In addition, two actuation schemes for the VGTM have been studied: actuation at each joint axis and actuation at the apex of each triangular element. The motor requirements for each scheme have been obtained and compared. A case study has been performed for a typical trajectory this manipulator.

An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

This paper describes how Fuzzy Set Theory and Fuzzy Numbers can be applied to the synthesis of planar and spatial mechanisms. The main advantage of using Fuzzy Set Theory over other methods of mechanism synthesis is that uncertainties in positions, rotations and link lengths can be quantified using the concept of membership functions. A membership function is an explicit representation of the deviation of the value of a parameter from its specified value. Numerical examples include the synthesis of a four-bar path generating mechanism with uncertain prescribed timing as well as uncertain path points and the RSSR spatial function generating mechanism. This work is expected to be a significant contribution to optimal mechanism design.

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.