Construction of a Six-Degrees-of-Freedom Parallel Manipulator With Three Planarly Actuated Links

The construction of a new type of a six-degrees-of-freedom parallel robot is presented in this paper. Coordinated motion of three planar motors, connected to three fixed-length links, produces a six-degrees-of-freedom motion of an output link. Its extremely simple design along with much larger work volume make this high performance-to-simplicity ratio robot very attractive.

A New Approach for Curvatures of Conjugate Surfaces

A new and general approach for curvatures of conjugate surfaces is provided in this paper. The main characteristic of the approach is that relative curvatures and geodesic torsions of the conjugate surfaces are directly calculated in terms of the normal curvatures and geodesic torsions of the generating surface on two non-orthogonal tangents of surface curvilinears in global surface system. In comparison with the current approaches that use two orthogonal tangents or the principal directions in local system at each calculating point, the approach developed in this paper has a simple calculating process and a simple computer program. Based on the curvature equations, sliding velocities and sliding ratios of the conjugate surfaces are studied. The approach is illustrated by a numerical example of a plane enveloping globoidal wormgear drive.

A New Method for Displacement Analysis of Multi-Loop Spatial Linkages Based on Ordered Simple-Opened-Chains

This paper presents systematically a new method for the displacement analysis (DA) of multi-loop spatial linkages (MLSLs) based on ordered simple-opened-chains (SOCs). In performing DA, a MLSL is converted into not a set of base points, a set of isolated links or a tree with/without isolated links in common use, but a weakly coupled MLSL in this paper. The characteristics of the proposed method are: (a) The number of unknowns in the set of equations for displacement analysis (EDA) of a MLSL is reduced to the minimum; (b) All the possible configurations corresponding to a given set of inputs of a weakly coupled MLSL or a strongly coupled MLSL with the coupled degree k = 1 can be obtained quickly. As compared with the other two methods available to find all the solutions to the DA in the case of MLSL with k = 1, the proposed method is superior to the resultant method in that it is applicable to more complex MLSLs and superior to the continuation method in that it takes much less CPU time to find all the solutions; (c) The set of EDA can be formulated and solved automatically; and (d) The new approach makes it possible to perform the kinematic and kineto-static analyses in a unified and simplified way.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

A Multi-Purpose Off-Line Path Planner Based on an A* Search Algorithm

Efficient navigation of an autonomous mobile robot through a well-defined environment requires the ability of the robot to plan paths. An efficient and reliable planar off-line path planner has been developed that is based on the A* search method. Using this method, two types of planning are accomplished. The first uses a map of all known obstacles to determine the shortest-distance path from a start to goal configuration. The second determines the shortest path along a network of predefined roads. For the most complicated environment of obstacles and roads, a near-optimal piecewise-linear path is found within a few seconds. The planner can generate paths for robots capable of rotation about a point as well as car-like robots that have a minimum turning radius. For car-like robots, the planner can generate forward and reverse paths. This software is currently implemented on a computer controlled Kawasaki Mule 500 all-terrain vehicle and a computer controlled John Deere 690 excavator.

Design of a Two-Input Linkage-Based Motor

This paper proposes the use of a seven-bar linkage mechanism to obtain a multiply actuated motor. Design of two input mechanisms is presented involving two synthesis sub-tasks of input motion synthesis and dimensional synthesis. To this end a design methodology is presented based on the theory of small crank mechanisms. For the case of small motion, approximate equations are developed with the premise that as a result of small reciprocating motion of the input actuators, the motion of every link, with the exception of the output, is small. The motion, in turn, is expressed as a sum of an average and a small oscillatory angular motion about the average. A set of design equations are obtained from the approximate kinematic equations. The design methodology is exemplified using the synthesis of a seven-link mechanism with two translating inputs.

Workspace of a Gimbal With Joint Limits

An analytical formulation for determining the workspace of a point on a body suspended in a Gimbal mechanism is presented. Although the gimbal mechanism comprises three degrees of freedom, the resulting workspace is a region on a spherical surface. The constraint function of the underlying mechanism is studied for singularities using a row-rank deficiency condition of its constraint Jacobian. Singular curves on the resultant spherical surface are determined by a similar analytical criterion imposed on the system’s subjacobian, to compute a set of two joint singularities. These singular curves define regions on the spherical surface that may or may not be accessible. A perturbation technique is then used to identify singular curve segments that are boundary to the workspace region. The methodology is illustrated through a numerical example.

Analytical Criteria for the Analysis of Design Propagations in Mechanisms

A broadly applicable formulation for investigating design propagations in mechanisms is developed and illustrated. Analytical criteria in terms of the variations of joint position vectors and orientation matrices for planar and spatial mechanisms are presented. Mechanisms are represented using graph theory and closed loops are converted to a tree-like structure by cutting joints and introducing new constraints. The Jacobian matrix in Cartesian space is then transformed to Joint coordinates space. Two cases are considered: a pair of bodies remain connected by one joint after cutting additional joints and a pair of bodies are disconnected after cutting joints. Using this method, a designer has the ability to study the propagated effect of changing a design variable on the design. The presented formulation is validated through a numerical example of a McPherson strut suspension system. The system is analyzed and an assembled configuration is computed after a change in design.

Leg Lift During Non-Overconstrained Pseudo-Static Walking

A non-overconstrained pseudo-static walking machine has 1 leg joint under position control for every degree-of-freedom of the body. When 1 joint is position controlled on each of 6 legs, leg lift during a step results in 1 unregulated degree-of-freedom of the body. A second joint in one of the 5 legs that maintain contact with the ground must be switched to active position control at the same time that a foot is lifted. In theory any passively controlled joint in the 5 supporting legs may be chosen. However the requirement that no leg be in tension and practical limits on torques available from joint actuators severely restrict choice of both additional joint to actively position control and possible body positions where legs can be lifted.

A Methodology for the Configuration Synthesis of Machining Centers With Automatic Tool Changer

The purpose of this paper is to present a design methodology for the configuration synthesis of machining centers with automatic tool changer to meet the required topology and motion characteristics. According to the concept of coordinate systems, graph theory, generalization, specialization, and motion synthesis, this design methodology is proposed and computerized, and the machining centers with automatic tool changer up to eight links are synthesized. As the result, for the machining centers with drum type tool magazine, the numbers of configurations of machining centers with 6, 7, and 8 links are 2, 13, and 20, respectively. And, for the machining centers with linear type tool magazine, the numbers of configurations of machining centers with 5, 6, 7, and 8 links are 1, 5, 20, and 60, respectively. Furthermore, this work provides a systematic approach for synthesizing spatial open-type mechanisms with topology and motion requirements.