Open Kinematic Chain Research Articles

Haptic Manipulation of Deformable Objects in Hybrid Bilateral Teleoperation System

The aim of this work is the integration of a virtual environment containing a deformable object, manipulated by an open kinematical chain virtual slave robot, to a bilateral teleoperation scheme based on a real haptic device. The virtual environment of this hybrid bilateral teleoperation system combines collision detection algorithms, dynamical, kinematical and geometrical models with a position–position and/or force–position bilateral control algorithm, to produce on the operator side the reflected forces corresponding to the virtual mechanical interactions, through a haptic device. Contact teleoperation task over the virtual environment with a flexible object is implemented and analysed.

Local dexterity analysis for open kinematic chains

Two methods for determining the dexterity of manipulator arms are presented. A numerical method is illustrated for determining all possible orientations of the end-effector of an open kinematic chain based upon a row-rank deficiency of the sub-Jacobian of the kinematic constraint equations. This numerical method has been adapted from a theory for determining the accessible output set for planar and spatial manipulators. Boundaries of regions representing orientation solutions are mapped using continuation algorithms. One-dimensional curves in three-dimensional space are traced. Orientations of the manipulator end-effector at a point are studied (local dexterity). Only local dexterity solutions can be found. A second analytical method is also presented which determines the global dexterity of the system. This method relies upon determining all singularities of the system and identifying singular surfaces and singular curves. Regions of singular surfaces that are boundaries are identified and intersected with a service sphere. This method, however, although analytical and accurate, has many limitations. The two methods are compared via implementation into a six degree of freedom manipulator.

Dynamic simplification of three degree of freedom manipulators with closed chains

A method is presented for designing manipulators to have simplified dynamics. It is based on adding a link group to an open kinematic chain to form a closed chain without changing the degrees of freedom of the open chain. The mass property of the link group is designed to make the closed chain have a diagonal inertia matrix. The conditions of mass distribution are derived under which the inertia matrices become diagonal. The advantage of the proposed method is that the manipulator dynamics can be treated as a decoupled linear system thereby greatly simplifying the control implementation. As examples of the technique we apply it to the design of a 3 DOF planar manipulator and a 3 DOF spatial manipulator.

Identification of inertial and friction parameters for excavator arms

A novel yet simple approach for experimental determination of the link (mass and inertia-related) parameters and friction coefficients is developed for a typical excavator arm. The parameters are needed for indirect measurement of the external forces, compensation for the link weights in the operator's hand in a force-feedback teleoperation setup, impedance control of the arm, simulation of the manipulator dynamics, and model-based fault detection. Treating the machine arm as an open kinematic chain, its dynamic equations are presented symbolically. The static torque equations are derived from these equations and the gravitational parameters are defined accordingly. A new method for decoupled estimation of the gravitational parameters from static experiments is presented. Furthermore, the arm dynamics are expressed in a form which is linear in the inertia and friction-related parameters. The results obtained show that the identified model predicts the joint torques, in both static and dynamic conditions, with a very good accuracy.

Coordinate-invariant algorithms for robot dynamics

We present, using methods from the theory of Lie groups and Lie algebras, a coordinate-invariant formulation of the dynamics of open kinematic chains. We first re-formulate the recursive dynamics algorithm originally given by Park et al. (1995) for open chains in terms of standard linear operators on the Lie algebra of the special Euclidean group. Using straight forward algebraic manipulations, we then recast the resulting algorithm into a set of closed-form dynamic equations. We then reformulate Featherstone's (1987) articulated body inertia algorithm using this same geometric framework, and re-derive Rodriguez et al.'s (1991, 1992) square factorization of the mass matrix and its inverse. An efficient O(n) recursive algorithm for forward dynamics is also extracted from the inverse factorization. The resulting equations lead to a succinct high-level description of robot dynamics in both joint and operational space coordinates that minimizes symbolic complexity without sacrificing computational efficiency, and provides the basis for a dynamics formulation that does not require link reference frames in the description of the forward kinematics.

A STRUCTURAL FLEXIBILITY TRANSFORMATION MATRIX FOR MODELLING OPEN-KINEMATIC CHAINS WITH REVOLUTE AND PRISMATIC JOINTS

A general approach to systematically derive the equations of motion of flexible open-kinematic chains is presented in this paper. The methodology exploits the serial characteristics of the kinematic chain by complementing the 4×4 Denavit–Hartenberg transformation matrix with a 4×4 structural flexibility matrix. The latter is defined based on a floating coordinate system which rendered the formulation applicable to both prismatic and revolute joints. The versatility of the approach is demonstrated through its implementation to formulate forward kinematic problems of manipulators with revolute and prismatic joints. Moreover, the proposed flexibility matrix is used in the development of a dynamic model for a compliant spherical robotic manipulator. This task has a dual purpose. First, it demonstrates how the flexibility matrix can be implemented in a systematic approach for deriving the equations of motion of an open-kinematic chain that account for the axial geometric shortening, the torsional vibration, and the in-plane and out-of-plane transverse deformations of the compliant member. Second, the inclusion of the torsional vibration in the equation of motion serves to broaden the scope of previous research work done on modelling open-kinematic chains. The formulation can now address dynamic problems that are not limited to the positioning but are also concerned with the orientation of rigid body payloads as they are being manipulated by robotic manipulators. The digital simulation results exhibit the interaction between the torsional vibration and the rigid body motion of the arm. Furthermore, they demonstrate a strong coupling effect between the torsional vibration and the transverse deformations of the arm whenever the payload is not grasped at its mass center by the gripper.

Dynamic control of free-floating coordinated space robots

The position and force control of coordinated robots mounted on spacecraft, manipulating objects with closed kinematic chain constraints, represents an important class of control problem. In this article, the kinematics and dynamics of free-floating coordinated space robotic system with closed kinematic constraints are developed. An approach to position and force control of free-floating coordinated space robots with closed kinematic constraints is proposed for the first time. Unlike previous coordinated space robot control methods which are for open kinematic chains, the method presented here addresses the main difficult problem of control of closed kinematic chains. The controller consists of two parts, position controller and internal force controller, which regulate, respectively, the object position and internal forces between the object and end-effectors. The stability of the closed-loop coordinated robotic system is analyzed using the error models of the object position and internal forces. It is proved that the errors in the object position and internal forces asymptotically converge to zero under the assumption of exact kinematic and dynamic models. © 1998 John Wiley & Sons, Inc.

構造変化を伴うリンク系の動力学計算法とヒューマンフィギュアの運動計算

This paper discusses the dynamics computation of structure-varying kinematic chains which imply mechanical link systems whose structure may change from open kinematic chain to closed one and vice versa. The proposed algorithm can handle and compute dynamics and motions of any rigid link systems in a seamless manner without switching among algorithms. The computation is developed on the foundation of the dynamics computation algorithms developed in robotics, which is inherently superior in efficiency due to explicit use of the generalized coordinates to those used in the general purpose motion analysis software. The structure varying kinematic chains are commonly found in computing human and animal motions. The established computation will provide the general algorithmic foundation of the computation of motion and control of humanoid robots and CG human figures.

Dynamic modelling of a four-legged robot

A unified dynamic modelling approach of closed and/or open kinematic chain mechanisms is established. It is based on the use of the Newton-Euler formalism and the explicit formulation of kinematic holonomic constraints for the closed loop mechanisms. The approach is then applied to derive the dynamic modelling of a four-legged robot adopting a walking gait. The different movement sequences of the gait are analysed in order to calculate the all necessary terms in the dynamic equations of the quadruped robot.

A robotically assisted munition loading system

AbstractDue to the reliance upon manual operations, conventional loading of munitions on tactical arcraft has several deficiencies including inefficient manpower and time utilization; accident potential; exposure of crew members to chemical, biological, and nuclear agents; and visual obstruction. This article reports on the research and development of a full‐scale prototype robotic system called Robotically Assisted Munition Loading System (RAMLS) comprising a fine motion mechanism (FIMOM), a pose acquisition device (PAD), a manual controller, and a data acquisition and computing system. The FIMOM is a six‐degree‐of‐freedom (DOF) parallel mechanism driven by six hydraulic actuators and the PAD is a passive open kinematic chain mechanism having 6 DOF. The article describes the design and functions of the RAMLS components and presents results of experiments conducted to evaluate the RAMLS's performance. © 3995 John Wiley & Sons, Inc.

Dynamic analysis of manipulators with consideration of dry friction

The paper presents an application of an algorithm for the solution of the inverse dynamic problem of manipulators in order to calculate the dry friction forces in dynamic analysis of open kinematic chains. The analysis considers the two alternate phases of kinetic friction and stiction. An application of the algorithm is exemplified by the dynamic analysis of a drilling vehicle.

ドリフト項をもつ非ホロノミック機械の制御

A mechanism with more generalized coordinates than the number of actuators is said to be an underactuated mechanism. An open kinematic chain with unactuated joints lies in this category. The motion constraints of underactuated multi-link mechanisms are due to their dynamics and do not usually have even the first integral. Such nonholonomic systems are characterized by a nonlinear affine state equation with a drift term. In this paper, we discuss asymptotical stabilization and positioning control of a nonholonomic mechanism with drift.

Synthesis of guidance mechanisms

A classical problem in mechanism-synthesis is the guidance of a point Z along a given path with the coordinates x= x ( t), y= y ( t), ( t 1≦ t≦ t 2). An open kinematic chain OMX with two revolute pairs in O and M can solve this problem. The constrained motion of this mechanism can be realized by using: • Two hydraulic-cylinders including computer control as inputs; one of them between frame and first link, the other between the two moving links. • One input and geometrical elements for describing the given path exactly. Special disks and a flexible band complete the open chain to a constrained band-mechanism. Starting from a given path, it is shown how to synthesize a band mechanism which solves this problem. Some examples demonstrate the practical application of such band-mechanisms.

Dynamic analysis of balanced robot mechanisms

A comparison of dynamic behaviour of the unbalanced and balanced robot mechanisms is carried out. Two various ways of balancing are considered: balancing by masses (by adding counterweights and by link mass redistribution) and balancing by springs. Dynamic behaviour of the robot is studied on the basis of its motion simulation. A simple open kinematic chain structure (“PUMA” configuration), is used as a basic mechanism. Some comparisons are made with a mechanism of closed loop structure (“ASEA” mechanism).

Computational aspects of the product-of-exponentials formula for robot kinematics

In this article we investigate the modeling and computational aspects of the product-of-exponentials (POE) formula for robot kinematics. While its connections with Lie groups and Lie algebras give the POE equations mathematical appeal, little is known regarding its usefulness for control and other applications. We show that the POE formula admits a simple global interpretation of an open kinematic chain and possesses several useful device-independent features absent in the Denavit-Hartenberg (DH) representations. Methods for efficiently computing the forward kinematics and Jacobian using these equations are presented. In particular, the computational requirements for evaluating the Jacobian from the POE formula are compared to those of the recursive methods surveyed in Orin and Schrader (1984).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Network model approach to the analysis of multirigid-body systems

The mathematical model of a rigid body in three dimensional motion developed in [1] is used to formulate the equations of motion for the systems of rigid bodies connected to form a special type of open kinematic chain. In this interconnection pattern of rigid bodies, each rigid body is considered as a 3-port component, and for the sake of generality, initially no constraints are imposed on the joints used to interconnect the rigid bodies. The system is considered as an (m+1)-port component and the corresponding terminal equations are obtained in closed form. As an appliction of these equations, a three-link plane manipulator is considered.

Task dependent synthesis of some geometrical parameters of a robot mechanism

SUMMARYThis paper deals with the synthesis of a robot mechanism, which has an open kinematic chain structure. The aim of the synthesis is to find optimal mechanism link lengths and the elevation of the robot mechanism base, with respect to the arbitrary chosen task which is described in a task space.A mathematical model, which describes the problem and enables one to use a nonlinear optimization algorithm, was developed. The usefulness of the approach is demonstrated by the example of the Manutec r3 mechanism with a prescribed task for the robot's end-effector.

Kinematically redundant robots with flexible components

Open kinematic chain mechanisms consisting of a sequence of rigid or elastic links joined together by single-degree-of-freedom joints that may, depending on the model in question, undergo elastic deformation are considered. It is assumed that there is a base of any kinematic chain under investigation as well as tip to which a tool or end effector is attached. Several problems in planning motions for these kinematically redundant mechanisms are described. The goal is to exploit redundant degrees of freedom to minimize the dynamic effects of joint elasticity. It is shown that in order for a prescribed end effector trajectory to store no elastic energy, certain differential-algebraic equations must be satisfied. For a specific example, it is shown that fifth-order splines can be used to prescribe admissible work space paths which interpolate an arbitrary finite set of points. Simulations have also indicated that admissible fifth-order paths for the end effector that approximate a straight line segment arbitrarily closely can be found. >

Planar reorientation maneuvers of space multibody systems using internal controls

In this paper a reorientation maneuvering strategy for an interconnection of planar rigid bodies in space is developed. It is assumed that there are no exogeneous torques, and torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero in this paper. The maneuver strategy uses the nonintegrability of the expression for the angular momentum. We demonstrate that large-angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is briefly summarized. Specifications and computer simulations of a specific reorientation maneuver, and the corresponding control strategies, are described. I. Introduction I N this paper we develop a reorientation strategy for a system of N planar rigid bodies in space that are interconnected by ideal frictionless pin joints in the form of an open kinematic chain. Angular momentum preserving controls, e.g., torques generated by joint motors, are considered. The TV-body system is assumed to have zero initial angular momentum. Our earlier work1'2 demonstrated that reorientation of a planar multibody system with three or more interconnected bodies using only joint torque inputs is an inherently nonlinear control problem that is not amenable to classical methods of nonlinear control. The goal of this study is to indicate how control strategies can be explicitly constructed to achieve the desired absolute reorientation of the TV-body system. There are many physical advantages in using internal controls, e.g., joint torque controls, to carry out the desired multibody reorientation maneuvers. First of all, this control approach does not modify the total angular momentum of the multibody system. In addition, internal controls have obvious advantages in terms of energy conservation. Moreover, they can be implemented using standard electrical servo motors, a simple and reliable control actuator technology. The formal development in this paper is concerned with control of a multibody interconnection in space that has zero angular momentum. Although these results are formulated in a general setting, we have been motivated by several classes of specific problems. Several potential applications of our general results are now described. Manipulators mounted on space vehicles and space robots have been envisioned to carry out construction, maintenance, and repair tasks in an external space environment. These space systems are essentially multibody systems satisfying the assumptions of this paper. To carry out the desired tasks, they must be capable of performing a variety of reorientation maneuvers. Previous research on maneuvering of such space multibody systems has mainly focused on maneuvers that achieve desired orientation of some of the bodies, e.g., an end effector, whereas the orientation of some of the remaining bodies cannot be specified, at least using the methodologies employed.38 Using the approach suggested in this paper, maneuvers that achieve any desired reorientation for all of the

The Application of Open and Closed Kinematic Chain Exercises in Rehabilitation of the Lower Extremity

The goal of rehabilitation is to return patients to their preinjury level of function. This task is achieved by restoring specific parameters of function that include joint range of motion (ROM), muscle performance (i.e., torque, work, power, time rate of tension development), soft tissue flexibility, proprioception/kinesthesia/balance, agility, and cardiovascular conditioning. Several methods are used by clinicians to restore function, including modalities and manual therapy. A key element, however, is the application of resistive exercises. The implementation and progression of exercises employed by the clinician may affect the final outcome. Exercises are used to isolate muscle action over one joint in a cardinal plane of movement. Other exercises incorporate synergistic action of muscle groups over multiple joints, using multiplanar movements. Ideally, treatment should incorporate a variety of exercises to achieve optimum rehabilitation. To facilitate this process, the rehabilitation specialist should understand basic concepts ofhuman kinesiology, as well as anatomy and the physiology of soft tissue healing. The purpose of this article is to: define terms associated with human movement; discuss kinematic-chain exercises; review rehabilitation principles and exercise progression; and incorporate this information into case studies. TERMINOLOGY