Closed-chain Mechanism Research Articles

A new instantaneous center analysis methodology for planar closed chains via graphical representation

Instantaneous center (IC) analysis of a mechanism is very important in mechanism analysis, since the analysis gives intuition about the global movement of the mechanism, and the analysis also makes the numerical analysis of velocities faster. Previous IC analysis methods have used geometrical information from the mechanism configuration. Such methods have disadvantages of complexity in calculation and difficulty determining the direction of linkage movement due to geometric complexity. This research suggests a new IC analysis method for planar closed chains. The proposed method determines the IC simply from the relation between joint velocities based on graphical representation. Twists in screw theory are used to define the joint velocities in a closed chain and also to calculate the IC. Three different kinds of mechanisms are analyzed by the method: a four-bar mechanism, slidercrank mechanism, and a multiple closed-chain mechanism composed of four-bar and slider-crank mechanisms. The analysis methodology can be applied to calculate the ICs of various planar closed chains.

Design and optimization of a dual quadruped vehicle based on whole close-chain mechanism

A new “whole close-chain mechanism” concept is proposed for the design of the modular legged unit of walking vehicles. Based on this concept, the walking vehicle called dual quadruped vehicle is developed and constructed. The vehicle designed as an omnidirectional carrying platform contains two identical single-driven quadruped mechanisms. The details of the design procedure are given, including the single close-chain legged mechanism, the modular legged unit, and the dual quadruped vehicle. The construction description of the single leg is presented. With the optimum design of the whole close-chain legged mechanism, the two foot-point characteristic trajectories are investigated. Based on the strategies of the legged module integration, the best phase configuration in pitching movement and the steering analysis are discussed and illustrated. Dynamic simulations and experiments are performed to verify the validity of the theoretical analysis of the new concept and the maneuverability of the vehicle prototype.

Independent force and position control for cooperating manipulators handling an unknown object and interacting with an unknown environment

This paper presents a unified framework for system design and control in cooperative robotic systems. It introduces a highly generalized cooperative system configuration that involves any number of manipulators grasping a rigid object in contact with a deformable working surface whose real physical parameters are unknown. The dynamics of the closed chain mechanism are expressed based on the object׳s center of mass (CoM), and different robust controllers are designed for position and force control subspaces. The position controller is composed of a sliding mode control term, and it involves the position and velocity feedback of an end-effector, while the force controller is developed based on the highest derivative in feedback methodology. The force controller does not use any derivation of the force signal or internal force controller induced in the system, and it appears to be suitable for practical implementation. Using a Lyapunov stability approach, the controller is proven to be robust with varying system dynamics. The position/orientation and the force errors are also demonstrated to asymptotically converge to zero under such conditions. The simulation results for two-joint arms moving a rigid object are presented to validate the theoretical results.

Optimal balancing of slider-crank servomechanism: closed-loop optimal position control approach

Minimisation of shaking forces in mechanisms is an important issue in industry due to its destructive vibrations and acoustical disturbances. Practically, it may be impossible to eliminate the shaking forces because of many factors such as unfeasible counterweights and/or counter-rotators. However, it can be minimised. This paper presents a novel method, based on the closed-loop optimal control theory to indirectly minimise the shaking forces and input torques. To this end, the integrated design method is extended to closed-chain mechanisms. The proposed method is applied on a nonlinear position control problem. A slider-crank mechanism is utilised to validate the control algorithms. However, the proposed method can be simply extended to other mechanisms. The results indicate an impressive improvement in the shaking force reduction with an insignificant change in the control performance.

Control and disturbances compensation in underactuated robotic systems using the derivative-free nonlinear Kalman filter

SUMMARYThe Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. The control problem for underactuated robots is non-trivial and becomes further complicated if the robot is subjected to model uncertainties and external disturbances. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system cannot be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is shown that one can estimate simultaneously external disturbance terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed Kalman Filter-based control scheme is tested in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.

The role of the scapula in preventing and treating shoulder instability.

The shoulder is a closed-chain mechanism that balances the mobility required by the ranges of motion in normal activities with the stability required to act as a stable ball and socket base for those activities. The scapula plays key roles in the closed-chain mechanism by being mobile enough to place the glenoid in optimal relation to the humerus to facilitate concavity/compression and by being a stable base for coordinated muscle activation to compress the humerus into the glenoid. Scapular dyskinesis alters these roles and is frequently present in many types of glenohumeral instability. It may create or exacerbate the abnormal glenohumeral kinematics in instability. Clinical evaluation methods can demonstrate scapular dyskinesis, and if dyskinesis is present, rehabilitation for the dyskinesis should be included in the non-operative, preoperative, or post-operative treatment. Rehabilitation for scapular dyskinesis can be performed by specific protocols and is more successful in muscle-predominant instabilities such as multidirectional instability and repetitive microtrauma instability. Level of evidence V.

Research on one Bio-inspired Jumping Locomotion Robot for Search and Rescue

Jumping locomotion is much more effective than other locomotion means in order to tackle the unstructured and complex environment in research and rescue. Here, a bio-inspired jumping robot with a closed-chain mechanism is proposed to achieve the power amplification during taking-off. Through actuating one variable transmission mechanism to change the transmission ratio, the jumping robot reveals biological characteristics in the phase of posture adjustment when adjusting the height and distance of one jump. The kinematics and dynamics of the simplified jumping mechanism model in one jumping cycle sequence are analysed. A compliant contact model considering nonlinear damping is investigated for jumping performance under different terrain characteristics. The numerical simulation algorithm with regard to solving the dynamical equation is described and simulation results are discussed. Finally, one primary prototype and experiment are described. The experimental results show the distance of jumping in the horizontal direction increases with the increasing gear ratio, while the height of jumping decreases in reverse. The jumping robot can enhance the capability to adapt to unknown cluttered environments, such as those encountered in research and rescue, using this strategy.

Concentric hole drilling in multiple planes for experimental investigation of five-axis reconfigurable precision hybrid machine

A five-axis machining center integrates two mechanical models: a three-degree-of-freedom parallel platform and traditional computer numerical control X–Y table. There is a trend for machining centers to be reconfigurable precision hybrid machine tools (RHMTs) for the fabrication of complex and precision products. Most industrial robots have open kinematic chains and serially connected links. A parallel manipulator is a closed-chain mechanism with two platforms (a base and moving platform) connected together by at least two independent kinematic chains. A parallel machine tool has the advantages of high rigidity, high precision, low inertia, and a simple mechanism. It is not easy to correct the errors in a five-axis machine tool. This paper focuses on the initial calibration of the static state errors, which consist of the errors from the component part machining, work-piece orientation, and mechanism combination. In an RHMT mechanism, a three-axis motion platform primarily controls the Z, α, and β freedoms. A laser displacement meter is fixed on the Z axis and measures the error in relation to the central position of the moving and fixed platforms when the x-y table is moved. The inverse kinematics of this mechanism will be revised, and an improvement will be made in the attitude precision of the moving platform. Finally, this paper discusses an experiment involving the drilling of concentric holes in multiple planes using an RHMT, and examines the cutting results from a coordinate measuring machine.

Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains

Abstract The dynamic model, particularly with reference to controller design, is an important issue in mechanical control and design. However, this model is often difficult to achieve in complex multi-closed-loop mechanisms, such as parallel mechanisms or forging manipulators. A new approach on the dynamic modeling of a multi closed-chain mechanism in a forging manipulator, which applies screw theory and the reduced system model, is proposed in this paper. The proposed method not only allows a straightforward calculation of actuator forces but also obtains the dynamic equation of the multi-closed-loop mechanism easily. The structure of dynamic model obtained is similar to that of standard Lagrangian formulations, which can extend vast control strategies developed for serial robots to complex multi-closed-loop mechanisms. A complex multi-closed-loop mechanism on a forging manipulator is decomposed into several serial mechanisms or simpler subsystems. The Lagrangian equations associated with each subsystem are directly derived from the local generalized coordinates of the sub-mechanisms. Jacobian matrices are used to interpret the differential equations of the sub-mechanisms into the generalized coordinate or the actuated pairs according to the D’Alembert principle. Hessian matrices are also applied to form a standard Lagrangian formulation. The screw theory is introduced to overcome the difficulties of solving transformed Jacobian matrices, thereby simplifying the calculation of the matrices. Computation difficulties of transformation matrices may decrease considerably by choosing suitable generalized coordinates instead of direct actuator variables. The full dynamics of the complex multi-closed-loop mechanism in a forging manipulator is presented. Simulations and experiments illustrate the reliability of the proposed method and the correctness of the dynamic model of the forging manipulator.

Elastodynamic behavior of balanced closed-loop mechanisms: numerical analysis of a four-bar linkage

This paper investigates the influence of two common techniques of static balancing on the dynamic performance of closed-chain linkages, by taking into account the flexibility of the mechanism components. The long-term goal of the research consists in enhancing the operation of parallel spatial robots by means of optimal balancing strategies. This contribution is primarily meant to provide the analysis method of the research and, for this purpose, it focuses on the planar four-bar linkage, intended as the simplest example of closed-chain mechanism. Firstly an original approach for the static balancing of planar linkages by means of constant-force generators is proposed. The implemented formulation, which permits to compute the balancing parameters of both counterweights and/or springs, is adopted for deriving a mass balanced and an elastically compensated variant of the studied four-bar linkage, respectively. Then the operation of the unbalanced linkage and its two balanced variants is numerically studied. The natural frequencies and mode shapes of these mechanisms are estimated by modal analysis, whereas the dynamic performance at different operating regimes is assessed by kineto-elastodynamic investigation and finally discussed.

Flexible Structural Design for Side-Sliding Force Reduction for a Caterpillar Climbing Robot

Due to sliding force arising from the closed chain mechanism among the adhering points of a climbing caterpillar robot (CCR), a sliding phenomenon will happen at the adhering points, e.g., the vacuum pads or claws holding the surface. This sliding force makes the attachment of the climbing robot unsteady and reducesthe motion efficiency. According to the new bionic research on the soft-body structure of caterpillars, some flexible structures made of natural rubber bars are applied in CCRs correspondingly as an improvement to the old rigid mechanical design of the robotic structure. This paper firstly establishes the static model of the sliding forces, the distortion of flexible bars and the driving torques of joints. Then, a method to reduce the sliding force by exerting a compensating angle to an active joint of the CCR is presented. The analyses and experimental results indicate that the flexible structure and the compensating angle method can reduce the sliding forces remarkably.

Adding sub-chain method for structural synthesis of planar closed kinematic chains

For at least the past five decades, structural synthesis has been used as a main means of finding better mechanisms with some predefined function. In structural synthesis, isomorphism identification is still a problem unsolved well, and to solve this problem is very significant to the design of new mechanisms. According to the given degree of freedom (DOF) and link connection property of planar closed chain mechanisms, vertex assortment is obtained. For solving the isomorphism problem, a method of the adding sub-chains is proposed with the detailed steps and algorithms in the synthesizing process. Employing this method, the identification code and formation code of every topological structure are achieved, therefore many isomorphic structures could be eliminated in time during structural synthesis by comparing those codes among different topological graphs, resulting in the improvement of synthesizing efficiency and accuracy, and the approach for eliminating rigid sub-chains in and after the synthesizing process is also presented. Some examples are given, including how to add sub-chains, how to detect simple rigid sub-chains and how to obtain identification codes and formulation codes et al. Using the adding sub-chain method, the relative information of some common topological graphs is given in the form of table. The comparison result is coincident with many literatures, so the correctness of the adding sub-chain method is convinced. This method will greatly improve the synthesizing efficiency and accuracy, and has a good potential for application.

Investigation of Positional Error in Two Degree of Freedom Mechanism With Joint Clearance

Closed chain mechanisms are used as robotic manipulators with special features. A planar two-DOF closed loop mechanism provides desired position of an end effecter in a confined workspace with two input motions. Position of end effecter depends on various factors including joint clearance. Positional accuracy forms important parameter for kinematic analysis of mechanism. This paper presents simple approach for quantifying error due to joint clearance in a two-DOF mechanism. Generalized scheme for positional deviation with and without clearance at joint is presented. Orientation of clearance links for maximum positional error is identified. Error at various positions is quantified in relation with clearance link length. Computer programming is used as a tool to workout positional analysis of mechanism. Results show that error is independent of magnitude of clearance, however, a function of location of end effecter in workspace.

Biped robot with triangle configuration

A new biped robot with a triangle configuration is presented and it is a planar closed chain mechanism. The scalability of three sides of the triangle is realized by three actuated prismatic joints. The three vertexes of the triangle are centers of three passive revolute joints coincidently. The biped mechanism for straight walking is proposed and its walking principle and mobility are explained. The static stability and the height and span of one step are analyzed. Kinematic analysis is performed to plan the gaits of walking on an even floor and going upstairs. A prototype is developed and experiments are carried out to validate the straight walking gait. Two additional revolute joints are added to form a modified biped robot which can follow the instruction of turning around. The turning ability is verified by experiments. As a new member of biped robots, its triangle configuration is used to impart geometry knowledge. Because of its high stiffness, some potential applications are on the way.

An improved kinematic model for calibration of serial robots having closed-chain mechanisms

SUMMARYMany industrial robots employ closed-loop actuating elements such as the parallelogram mechanism for increased stiffness. Modeling these manipulators for the purpose of calibration presents a challenge due to complex nonlinear couplings between parameters of the chains. The modeling method presented in this paper involves the integration of the open- and closed-loop elements whose errors can be resolved as linear functions of their parameters. As a result, the model is similar to that of a serial-link robot, which makes it possible to use existing well-defined calibration techniques in the area. Simulation and experimental studies on an industrial robot for verifying the correctness and effectiveness of the proposed model are also described.

Inverse Dynamics of a Redundantly Actuated Four-Bar Mechanism Using an Optimal Control Formulation

Abstract This paper presents an approach to estimating joint torques in a four-bar closed-chain mechanism with prescribed kinematics and redundant actuation, i.e., with more actuators than degrees of freedom. This problem has several applications in industrial robots, machine tools, and biomechanics. The inverse dynamics problem is formulated as an optimal control problem (OCP). The dynamical equations are derived for an open-chain mechanism, what keeps the formulation simple and straightforward. Sets of constraints are explored to force the three-link open-chain to behave as a four-bar mechanism with a crank rotating at a constant velocity. The controls calculated from the OCP are assumed to be the input joint torques. The standard case with one torque actuator is solved and compared to cases with two and three actuators. The case of two actuators presented the smallest peak and mean torques, using one specific set of constraints. Such torques were smaller than the solution obtained using an alternative method existing in literature that solves the redundancy problem by means of the pseudo-inverse matrix. Comparison with inverse dynamics solutions using well-established methods for the one-actuator closed-loop four-bar were equal. Reconstructed kinematical trajectories from forward integration of the closed-loop mechanism with the OCP obtained torques were essentially similar. The results suggest that the adopted procedure is promising, giving solutions with lower torque requirements than the regularly actuated case and redundantly actuated computed with other approaches. The applicability of the method has been shown for the four-bar mechanism. Other classes of redundantly actuated, closed-loop mechanisms could be tested using a similar formulation. However, the numerical parameters of the OCP must be chosen carefully to achieve convergence.

Properties of the Bennett Mechanism Derived From the RRRS Closure Ellipse

For many single-loop closed-chain mechanisms, mobility may be characterized by the closure of sets in the theory of Lie groups. The four-revolute (4R) Bennett mechanism remains a persistent exception, requiring the formulation and expression of solutions to the loop closure relations, either directly or indirectly through spatial geometric figures. The simpler loop closure relations of the revolute-revolute-revolute-spherical (RRRS) loop, however, place conditions on the mobility of the 4R mechanism. That loop closure in turn may be interpreted as the congruence of a pair of ellipses. This new result is applied to proving the uniqueness of the Bennett mechanism along with deriving conditions where it is free from singularities. Design parameters are also identified for overconstrained RRRS mechanisms with 1DOF that are neither plane nor line symmetric. Such mechanisms, however, place the S-joint along the revolute axis of an underlying Bennett mechanism.

A humanoid robot capable of carrying heavy objects

SUMMARYA new type of 28-DOF (degree of freedom) full-size humanoid robot, driven by a closed-chain type of joint actuation system, is developed in this paper. Each leg of the robot is composed of six joints, where three are at the hip, one is at the knee, and two are at the ankle. The robot has six joints for each arm, one balancing joint, and three joints for the head, with two cameras. The weight of the robot is 75 kg, and its height is 168 cm.The actuation systems of the pitching joint for the arms and legs of the robot are designed based on a closed-chain mechanism composed of four bar links driven by a ball screw, and each leg of the robot is designed to support 95 kg weight to include a 20 kg payload that can be carried by the robot arms having very light designs (with weight 8.5 kg), but each capable of carrying a 10 kg payload.An analysis of the closed-chain joint actuation systems of a light arm capable of handling heavy objects is performed, and the light arm is designed via finite-element method analysis performed using ANSYS. In addition, the kinematic analysis and the detailed structure of the arm and leg of the robot are performed.The main controller uses the ARM processor and a distributed controller for the leg joints is developed using the TMS320c2407 processor with the communications between the main and joint controllers being performed via the CAN system.Good performances of the proposed robot is demonstrated by presenting several experimental results; these include (1) experimentally handling a 13 kg payload, (2) through walking experiments of the robot supporting a 85 kg load, and (3) measurements of the arm and leg joint motors while performing walking experiments.

Orientation angle rotatability of planar serial n-link manipulators

This paper presents a new method of analyzing the orientation angle rotatability of a planar serial n-link manipulator by examining the rotatability of its virtual equivalent mechanism. Workspace orientation boundary region decomposition is proposed based on the polynomial discriminant derived from a serial three-link manipulator. Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace. By introducing a virtual equivalent mechanism, the open-chain kinematic problem is converted into a close-chain mechanism, and the Grashof-type condition is used to examine the rotatability of the end-effector link. The reachable position workspace can be divided into several Grashof intervals and non-Grashof intervals based on the extreme positions and singular configurations of a manipulator. The derived equations in this paper can be used to calculate the variation rule of the orientation angle workspace of any given planar serial n-link manipulator on the basis of its link parameters. The orientation angle rotatability of a seven-link serial manipulator is solved by the proposed method and graphical representations of the orientation angle workspaces are mapped onto a three-dimensional coordinate system. The theoretical approach has practical significance for the design of a highly dexterous serial n-link manipulator with proposed link relations.

Active Position and Vibration Control of a Flexible Links Mechanism Using Model-Based Predictive Control

In order to develop an efficient and fast position control for robotic manipulators, vibration phenomena have to be taken into account. Vibrations are mainly caused by the flexibility of manipulator linkages, especially when dealing with high-speed and lightweight robots. In this paper, a constrained model-based predictive control is employed for controlling both position and vibrations in a mechanism with high link flexibility. This kind of controller has so far been used mainly to control slow processes, but here simulation results that show its effectiveness in dealing with high-speed and nonlinear processes are presented. The mechanism chosen to evaluate the performances is a four-link closed chain mechanism laying on the horizontal plane and driven by a single torque-controlled electric motor.