Optimal Trajectory Resolution for the Coordination of Two Robots in Contact Operations

A new method is presented for the optimal coordination of a two-robot system performing contact operations. One of the robots carries a tool and performs the specific contact operation on a workpiece which is grasped and maneuvered by the second robot. The two robots move simultaneously relative to each other so that the tool maintains contact with the workpiece while moving along its prescribed trajectory at a constant speed. This prescribed trajectory, which is specified with respect to the workpiece frame, is thus resolved into a pair of conjugate trajectories, one for each robot, and specified in the world coordinate frame. This resolution process does not yield a unique solution, i.e. there exist an infinity of conjugate-trajectory pairs corresponding to a given tool trajectory. This paper presents a technique for resolving the original tool trajectory, where the robots’ conjugate trajectories are parameterized using polynomial functions. A method is then developed for selecting the optimal pair of conjugate trajectories on the basis of minimizing a given choice of cost function. This optimization is further enhanced by coupling it to a procedure for selecting the optimal layout of the robots within the workcell, resulting in the best possible solutions. Numerical simulation results support the validity of the proposed technique.

Optimal Design of a Six-Bar Linkage for an Anthropomorphic Three-Jointed Finger Mechanism

We treat the design of a three-jointed, anthropomorphic, finger mechanism for prostheses and robotic end-effectors. Based on the study of configurations for the human finger, we propose a six-bar linkage with one degree of freedom for the finger mechanism. A model of the fingertip displacement of the mechanism is derived by a vector analysis approach. We study the effects of joint friction on the transmission efficiency. By measuring the joint positions of a human finger, we develop a mathematical model of the pinching and holding configurations for the human finger. Optimal parameters for the finger mechanism are obtained by nonlinear programming based on motion posture, locus, transmission efficiency, and weight subject to geometric and bionic constraints. Simulations indicate that the mechanism is useful in a variety of prosthetic and robotic devices.

Real Time Trajectory Modification Using a Closed Form Solution

An on-line trajectory modification and path planning strategy is developed which will allow a robot to respond in an efficient manner to real time sensory input. The approach developed here eliminates the need for solving many equations by developing a closed form algorithm. It uses two fourth order curves for the transition phases with a constant velocity section in between. Although this is done by providing additional constraints to the curve, it makes the problem of determining the trajectory much easier to solve, while providing continuous higher derivatives. It also provides a safe and efficient way of modifying trajectories based on the robots joint rate limits, joint acceleration limits, jerk limits, and desired time interval between trajectory modifications for a 4-1-4 trajectory. This method involves the solution of one second order equation and is directed toward real time applications.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Workspace Evaluation of Stewart Platforms

The workspace and the dexterity of a Stewart Platform are effected by the choice of its major dimensions, actuators’ stroke and the kinematic constraints of its joints. An investigation of the effects of these parameters on workspace volume of the platform is presented. The obtained results were normalized so that these can be used as a design tool for the selection of dimensions, joints and actuators.

Die Producibility Evaluation Method

Given the design of a sheet metal component that is to be produced by pressworking, there can be more than one design for the die to produce that component. It will be desirable if a mechanism exists to identify the better of the design alternatives. A method referred to as Die Producibility Evaluation Method (DPEM) is presented in this paper to evaluate the design of a given pressworking die. The method involves identification and classification of the parameters involved in the design and operation of the pressworking die. These parameters are categorized as design cost factors and process cost factors. For a given die design, the design and process cost factors are identified and the results are tabulated in the DPEM table. In order to illustrate the method, a particular sheet metal component is chosen. A set of dies required to produce this component is then designed by a novice designer. This design is referred to as the initial design. The Die Producibility Evaluation Method is applied to the initial design, the DPEM table is updated, and an improved design is identified based on the evaluations recorded in the DPEM table. In order to provide a measure of quality, a second design is carried out under the guidance of an expert designer and is referred to as the reference design. It is shown that the improved design closely matches the reference design, thus illustrating the level of performance and applicability of the Die Producibility Evaluation Method.

A Synthesis Algorithm of Three-Revolute Manipulators by Means of the Workspace Contour Algebraic Formulation

A synthesis algorithm of general three-revolute open chain manipulators is proposed making use of an algebraic formulation of the workspace contour, which has been deduced in a previous paper. The algebraic form of the synthesis model allows to formulate some algebraic design equations and to discuss the number and the type of the multiple solutions.

A New Approach to Type Synthesis of Spatial Robotic Mechanisms

This paper presents a new approach for carrying out the type synthesis of spatial parallel platform-type mechanisms, used as robot manipulators. It takes into account the total mobility of the system and the partial mobility of its sub-mechanisms. The paper also provides the necessary and sufficient conditions for the mechanisms to function with specified end-effector freedoms, which are described in two theorems. The total number of possible mechanisms with given mobility and structure are tabulated. The work is based on a modified Grübler mobility criterion and also on the consideration of kinematic restraints.

Push-Pull Pair of Single Action Mechanisms to Preload Strut and Node Joints in the Robotic Assembly of Structures in Space

When strut and node components are used for truss construction or repair, an assembly problem occurs if a strut must fit between nodes whose separation distance is either more or less than the design specification. In such circumstances two actions would permit continued assembly: 1. Change strut length 2. Move the nodes. Variable length struts fit between nodes and (or) move them. They are preloaded at the joint against a reference length in an attempt to maintain the desired dimension. As a by-product they either pull the nodes together or push them apart. Most cannot do both, and are therefore characterized as “single action”; those that can do both are “double action”. Double action mechanisms are currently being used for robotic truss assembly because they solve the above stated crucial problem in both directions. Single action mechanisms tend to exhibit superior performance in all other categories. They benefit from the attributes that accompany their simplicity. The titled concept combines the major advantage of double action with the simplicity of single action. This is demonstrated with an example.

Predicting Force Redistributions on Walking Robots for Reliable Locomotion: Modeling and Experiments

A large number of walking robots walk with a statically-stable gait. A statically-stable walker has at least three feet that are in ground contact at any time. If there are more than three feet in ground contact, the normal (vertical) forces exerted by the ground on the feet of the walker are indeterminate, unless they are measured. Some walking robots may walk with more than three legs in ground contact in order to achieve greater stability. To ensure this stability it is desirable to predict how vertical forces passively redistribute underneath the feet during walker motions. Predictions of future foot forces can be used as a basis for accepting or rejecting any planned walker motion. Two methods — the least-squares method and the compliance method — for predicting this redistribution of forces in the face of static indeterminacy are presented in this work. Both methods are computationally efficient, and give reasonably accurate predictions, as verified by experiments on a walking robot.