Dynamic Analysis of Elastic Beam-Like Mechanism Systems

In this paper the dynamic behavior of beam-like mechanism systems is investigated. The elastic beam is modeled by finite rigid segments connected by joint springs and dampers. The equations of motion are derived using Kane’s equations. The nonlinear terms are linearized by first order perturbation about a system balanced configuration state leading to geometric stiffness matrices. A simple numerical example of a rotating cantilever beam is presented.

Allocation of Dimensional Tolerances for Multiple Loop Planar Mechanisms

A method is presented to determine tolerance bands for the dimensions of multiple loop planar mechanisms such that output motions will be kept within specified allowable limits. The kinematic equations of mechanisms are generated by combining various link groups. A preliminary set of estimated tolerance bands is calculated using an analytical technique. An optimization and checking routine is then employed to determine the set of input parameters which satisfies the prescribed output motion requirements. Examples have been included to illustrate the method.

Identification and Observability Measure of a Basis Set of Error Parameters in Robot Calibration

This paper presents a method of identifying a basis set of error parameters in robot calibration using the Singular Value Decomposition (SVD) method. With the method, the error parameter space can be separated into two: observable subspace and unobservable one. As a result, for a defined position error model, one can determine the dimension of the observable subspace, which is vital to the estimation of error parameters. The second objective of this paper is to study, when unmodeled error exists, the implications of measurement configurations in robot calibration. For selecting measurement configurations in calibration, and index is defined to measure the observability of the error parameters with respect to a set of robot configurations. As the observability index increases, the attribution of the position errors to the parameters becomes dominant and the effects of the measurement and unmodeled errors become less significant; consequently better estimation of the parameter errors can be obtained.

Optimum Synthesis of Thin-Walled Vibrating Beams With Coupled Bending and Torsion

This paper considers the optimum structural design of vibrating beams in which the inertial axes and the elastic axes are noncollinear. The condition of noncollinear axes exists in structures having unsymmetric cross-sections. For unsymmetric cross-sections the centroid and the shear center do not coincide. This results in coupling between some of the bending and torsional modes. This paper presents results for the simply supported and cantilever beams with a thin-walled channel cross-section. The minimization of the structural volume subject to multiple frequency constraints and its dual problem of maximization of the fundamental frequency subject to a volume constraint are considered. A quadratic extended interior penalty function with Newton’s method of unconstrained minimization is used in structural optimization. The structures considered have nonstructural masses besides their own mass.

Optimal Tooth Modifications for Spur and Helical Gears

A method for the simultaneous calculation of optimal tooth tip relief and tooth crowning for spur and helical gears is presented in this paper. The tooth profile modification is described by a linear function. Two types of crowning are introduced: linear and parabolic. The optimization of the tooth modifications is based on the following conditions: (1) The teeth are entering in mesh smoothly, without interference. (2) The load distribution factor is minimized. A computer program is developed for the calculation of the optimal tooth tip relief and crowning for spur and helical gears. By using this program the influence of type and length of optimal crowning and length of tooth tip relief on load distribution factor is investigated. Also, the influence of gear parameters on optimal tooth profile modification is discussed. On the basis of the obtained results, by regression analysis an equation is derived for the calculation of the optimal tooth tip relief.

Comparison of the Dynamics of Conventional and Worm-Gear Differentials

The differential mechanism has been used for many years and a variety of unique designs have been developed for particular applications. This paper investigates the performance of both the conventional bevel-gear differential and the worm-gear differential as used in vehicles. The worm-gear differential is a design in which the bevel gears of the conventional differential are replaced by worm gear/worm wheel pairs. The resultant differential exhibits some interesting behavior which has made this differential desirable for use in high performance and off-road vehicles. In this work, an Euler-Lagrange formulation of the equations of motion of the conventional and worm-gear differentials allows comparison of their respective behavior. Additionally, each differential is incorporated into a full vehicle model to observe their effects on gross vehicle response. The worm-gear differential is shown to exhibit the desirable characteristics of a limited-slip differential while maintaining the conventional differential’s ability to differentiate output shaft speeds at all power levels.

Model Based Rigid Body Guidance in Presence of Nonconvex Geometric Constraints

This paper presents an efficient algorithm for guidance of a convex rigid body in-between nonconvex polygonal objects in a Computer-Aided Design (CAD) environment. A shrinking procedure is used that separates the kinematic from the shape constraints by reducing the problem to that of guidance of a line segment in an expanded environment. A slicing technique together with an algorithm for decomposition of the interface channel between the nonconvex objects is used to generate the motion program for the line segment. The results can be applied to model based guidance of mobile robots or automatic motion planning for robot manipulators.

Tolerance Volume Due to Joint Variable Errors in Robots

The locational uncertainty of a manipulator is largely due to the errors of the joint variables. But these errors cannot be easily compensated for because they are dependent on the operation (i.e., robot-configuration). Motivated by the need to conduct precision engineering and the intellectual curiosity of geometric uncertainty, the probabilistic tolerance volume due to joint errors is investigated. By defining the locational uncertainty in Cartesian space as a tolerance volume, the investigation focuses on the automatic generation of the tolerance volume from a given confidence level. For this purpose, the linear mapping form Δq space to Δd space through Jacobian matrix is analyzed probabilistically. Probabilistic approach is advantageous since the tolerance volume by the deterministic approach is found to be unnecessarily large. With the assumption of normality of joint variables, this paper begins with the computation of the confidence level for a given tolerance volume. A fast analytic procedure, which gives a considerable time-reduction compared to the commonly used Monte-Carlo simulation, is presented. Based on the monotonic relation between confidence level and tolerance volume, the procedure is used to generate the tolerance volume covering the desired confidence level. The scheme is tested with the six degrees-of-freedom Stanford manipulator and shows a significant (more than 5 times) reduction in the size of the tolerance volume with a 0.3 percent probability of error.

An Efficient Rate Allocation Algorithm in Redundant Kinematic Chains

This paper addresses a basic problem which arises in the coordination of serial chain manipulators, namely, that of decomposing a given end effector velocity state into a set of joint rates. Such a problem is indeterminate for manipulators with kinematic redundancy. A novel method of solving the rate distribution problem for the class of fully revolute-jointed, serial manipulators is developed. The technique is an extension of the axial field solution scheme developed initially for solving the force allocation problem in a statically indeterminate parallel chain system. The basis of the solution method lies in the dualities of velocity and force systems between series and parallel mechanisms. The method offers an efficient means of rate coordination and is especially useful in the control of manipulators with high degrees of redundancy. Two examples have been given for illustration. It is shown that the minimum norm solution, obtainable commonly from pseudoinverse, can also be achieved using this new efficient algorithm.

A Strategy of Wave Gait for a Walking Machine Traversing a Rough Planar Terrain

The performance of a legged system is closely related to the adopted gait. Among the many available gaits, the wave gait possesses the optimum stability [1–3] and has been applied to walking on perfectly smooth terrain. The follow-the-leader (FTL) gait has the least demands for foothold selection and is the most suitable for walking on rough terrain [14]. In this paper, a strategy of wave gait which enables a hexapod to traverse two-dimensional, rough terrain is developed. This strategy applies a quasi FTL mode in walking and hence it has the advantages of both wave gait (optimum stability) and FTL gait (easy control on rough terrain). During walking, the legs move according to the wave gait and the two forelegs are adjusted to avoid forbidden areas. The maximum foot adjustment is determined by the current foot positions and the foot positions in the following one or two step(s). In order to improve the stability, different methods of foot adjustments and body adjustments are evaluated and integrated into the strategy. Finally, this strategy is verified by using computer graphics simulations.