End-effector Point Research Articles

Effective workspaces of parallel robots

AbstractAn approach for calculating the effective workspaces of parallel mechanisms has been considered in this paper. The effective workspace is a set of reachable by the end-effector points, where an important parameter (or parameters) from the point of view of operation is not higher than critical. In this article, the speed and torque in the drive and the stiffness of the mechanism are considered as such parameters. An approach to determining the appropriate effective workspace is presented for each parameter. The optimization process, which is based on presented methods, allows one to choose basic technical solutions of the designed robot: the links (lengths and cross-sections), the drives, and types of hinges, which guarantee its operability at the specified operational characteristics. Case studies of a delta robot with four degrees of freedom and a planar five-bar mechanism are presented for testing these approaches. The presented methods are of great practical importance because it uses movement parameters or operational characteristics that are decisive for this mechanism and have clear physical meaning.

On the Effect of the End-effector Point Trajectory on the Joint ‎Jerk of the Redundant Manipulators

This paper is focused on investigating the joints jerk of industrial serial redundant manipulators with 6 degrees of freedom (6-DOF) under the variation of the end-effector point (EEP) trajectory in the workspace. The EEP trajectories are initially built in the basic planes because of their simplicity, verification and experimentation are smooth, and most of the actual welded structures are performed on these basic planes. The jerk is determined by solving the inverse kinematics problem of the redundant system. This problem is solved based on the algorithm which is used for adjusting the increments of the generalized coordinate vector (AGV). The efficiency of this algorithm is shown through the error between a given trajectory and the recalculated trajectory through the forward kinematics problem. The result of this study allows us to evaluate the effect of the change of the trajectory on the kinematics characteristics of the robot in general and the jerk of the joints in particular. On the other hand, these results can be used as the basis for planning the EEP trajectory for redundant robots, developing algorithms to reduce joint jerky, increase the life of robot systems, and improve the accuracy of the redundant robot movement.

Dynamic Modeling and Control of a Flexible Link Manipulators with Translational and Rotational Joints

Flexible link manipulators are widely used in many areas such the space technology, medical, defense and automation industries. They are more realistic than their rigid counterparts in many practical conditions. Most of the investigations have been confined to manipulators with only rotational joint. Combining such systems with translational joints enables these manipulators more flexibility and more applications. In this paper, a nonlinear dynamic modeling and control of flexible link manipulator with rigid translational and rotational joints is presented. This model TR (Translational-Rotational) is developed based on single flexible link manipulator with only rotational joint. Finite element method and Lagrange approach are used to model and build equations of the motion. PID controller is designed with parameters (Kp, Ki, Kd) which are optimized by using Particle Swarm Optimization algorithm (PSO). Errors of joints variables and elastic displacements at the end-effector point are reduced to warrant initial request. The results of this study play an important role in modeling generalized planar flexible two-link robot and in selecting the suitable structure robot with the same request.

VELOCITIES AND ACCELERATIONS AT THE 3R ROBOTS

The paper presents an original method to determine the velocities and the accelerations at the MP-3R structures. At the 3R structure (spatial) are known (imposed) the angular speeds of actuators and must be determined the velocities and the accelerations of the endeffector point M. Starting from the MP-3R direct kinematic positions system, deriving these relations system in function of the time, one time and then a second time (the second derivation) one obtains first the system velocities, and second time the accelerations of the point endeffector M. The system which must be solved has three equations and three independent parameters to determine. Constructive basis is represented by a robot with three degrees of freedom (a robot with three axes of rotation). If one study (analyzes) an anthropomorphic robot with three axes of rotation (which represents the main movements, absolutely necessary), it already has a base system, on which one can then add other movements (secondary, additional). All calculations were arranged and in the matrix form.

Velocities and Accelerations at the 3R Mechatronic Systems

This article presents an original method to determine the speeds and accelerations to structures MP R-3 The structure of the 3R (space) are known (required) rotation speeds of the triggers and must be determined speeds and accelerations of the endeffector M. Starting from the positions of direct kinematic system MP R-3deriving these system of relations in depending on the time, once and then a second time (the second derivation) is first obtains the speeds of the system and for the second time the accelerations endeffector point M. System on which must be resolved has three equations and three independent parameters to determine. Constructive basis is represented by a robot with three degrees of freedom (a robot with three axis of rotation). In the case where a study (analysis) a robot anthropomorphic with three axis of rotation (which represents the main movements, it is absolutely necessary), already has a system of the basis on which it can add other movements (secondary,). All calculations have been arranged and in the form of the array.

Inverse Kinematics

Inverse kinematics is the process of converting a Cartesian point in space into a set of joint angles to more efficiently move the end effector of a robot to a desired orientation. This project investigates the inverse kinematics of a robotic hand with fingers under various scenarios. Assuming the parameters of a provided robot, a general equation for the end effector point was calculated and used to plot the region of space that it can reach. Further, the benefits obtained from the addition of a prismatic joint versus an extra variable angle joint were considered. The results confirmed that having more movable parts, such as prismatic points and changing angles, increases the effective reach of a robotic hand.

Active Joint Stiffness Regulation to Achieve Isotropic Compliance in the Euclidean Space

This paper is dedicated to the relationship between the external force applied on a point of a robot end-effector and its consequent displacement in static conditions. Both the force and the displacement are herein considered in the Euclidean space E(3). This fact represents a significant simplification of the approach, since it avoids some problems related to the absence of a natural positive definite metric on the Special Euclidean Group SE(3). On the other hand, such restriction allows the method to find closed-form solutions to a large class of problems in robot statics. The peculiar goal of this investigation consists of setting up a procedure which guarantees at least one pose at which any force applied (in E(3)) to an end-effector point is always parallel to its consequent displacement (also in E(3)). This property, which will be referred to as isotropic compliance in E(3), makes the robot tip static behavior uniform with respect to all directions, namely, isotropic, although not homogeneous, since it holds only in some poses. Achieving isotropic compliance in E(3) is a task more general than the classical problem of finding a pose with unit condition number, which does not include the case of different elements in the diagonal joint stiffness matrix. For this reason, the object of the present investigation could not be furtherer simplified to the classical kinetostatic problem in terms of the jacobian matrix alone. The paper reveals how the force–displacement parallelism can be achieved by using a method based on a simple proportional-derivative (PD) controller strategy. The method can be applied when the passive and active stiffness act, on the joints, either in parallel or in series, and the magnitude of the displacement response can be chosen by imposing appropriate values for the overall joints compliance. Results show that for the three analyzed examples, namely, the RR, RRP, and RRR manipulators, with arbitrary lengths of the links, there is, at least, one pose for which the sought property is achieved.

A new solution to the inverse position analysis of the redundant serial robot

A new solution to the inverse position analysis of the redundant serial robot is presented. The inverse position analysis problem of the redundant serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least square problem with the analytic form of a new Jacobi matrix. In this way, the inverse solution of the redundant serial robot can be searched out quickly under the desired precision when the positions of the three non-collinear end effector points are given. The inverse position analysis of the 7R redundant serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.

Finger reach envelope using the marching cubes method

Reach envelope is commonly used not only to evaluate hand function but also to assess joysticks, tools for ergonomic design. A digital human simulation suite has been developed recently which includes customised hand model, kinematics, grasping, discomfort assessment, finger posture prediction, biomechanics, etc. The reach envelope is one of the hand capabilities in this hand simulation suite. This paper mainly focuses on the digital hand model and the procedure for implementing the marching cube method for generating finger and hand reach envelopes. The digital hand model has 25 degrees of freedom (DOF) and can realistically simulate all possible movements of each finger in three-dimensional space. The method involves the following steps: 1) select an end-effector (point of interest); 2) select DOFs to freeze; 3) choose scalar field resolution; 4) generate point cloud; 5) generate 3D scalar field; 6) generate mesh. The marching cubes method for reach envelope is much faster than other methods presented in the literature. The developed package can be used to generate the reach envelope for any point on any finger.

Adaptive Real-time Predictive Compensation Control for 6-DOF Serial Arc Welding Manipulator

Because of long driving chain and great system load inertia, the serial manipulator has a serious time delay problem which leads to significant real-time tracking control errors and damages the welding quality finally. In order to solve the time delay problem and enhance the welding quality, an adaptive real-time predictive compensation control(ARTPCC) is presented in this paper. The ARTPCC technique combines offline identification and online compensation. Based on the neural network system identification technique, the ARTPCC technique identifies the dynamic joint model of the 6-DOF serial arc welding manipulator offline. With the identified dynamic joint model, the ARTPCC technique predicts and compensates the tracking error online using the adaptive friction compensation technique. The ARTPCC technique is proposed in detail in this paper and applied in the real-time tracking control experiment of the 6-DOF serial arc welding manipulator. The tracking control experiment results of the end-effector reference point of the manipulator show that the presented control technique reduces the tracking error, enhances the system response and tracking accuracy efficiently. Meanwhile, the welding experiment results show that the welding seam turns more continuous, uniform and smooth after using the ARTPCC technique. With the ARTPCC technique, the welding quality of the 6-DOF serial arc welding manipulator is highly improved.

A successive approximation algorithm for the inverse position analysis of the general serial manipulators

A new fast numerical algorithm for the solution of the inverse position analysis of the serial manipulator is presented. With the algorithm, the inverse solution of the general serial manipulators can be achieved quickly under the desired precision when we know the position of the three non-collinear end-effector points, which is much easier to be measured than the orientation of the end-effector. The difference between the new numerical algorithm and the general iterative method is that it can search out the solution when the manipulator is at the singular configuration; and the initial configuration used in the successive approximation process may also be the singular configuration. So the convergence domain is bigger than that of the general iterative method. The position analysis of the general 6R serial manipulator is illustrated in the literature as an example and the simulation results to verify the efficiency of the proposed algorithm. Since the three non-collinear end-effector points can be selected at random, the algorithm can be applied to any other serial manipulator.

A new numerical algorithm for the inverse position analysis of all serial manipulators

A new fast successive approximation algorithm for the solution of the inverse position analysis of a general serial manipulator is presented. With the algorithm, we can search out the inverse solution of the serial manipulator quickly under the desired precision when the position of the three non-collinear end effector points is given. The position analysis of the 7R redundant serial manipulator is illustrated in the literature as an example. The simulation results verify the efficiency of the proposed algorithm. Since the three non-collinear end effector points can be selected at random, the algorithm can be applied to any other type serial manipulator.

Force transmission analyses with dimensionally homogeneous Jacobian matrices for parallel manipulators

To avoid the unit inconsistency problem in the conventional Jacobian matrix, new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points was presented (Kim and Ryu, 2003). This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived unit consistent Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.

Workspace analytic determination of two similar translational parallel manipulators

The design of a parallel manipulator for a given workspace would be greatly facilitated, if the analytic expressions of the hypersurfaces bounding the workspace were available. In translational parallel manipulators (TPMs), the hypersurfaces bounding the workspace are actually three-dimensional surfaces, which are the geometric locus of all the positions assumed by an end-effector point when the TPM reaches the workspace borders. These surfaces can be represented in a Cartesian reference system fixed to the frame. This paper studies the workspace of two TPMs, that have the same closure equations and workspace when a few geometric conditions are satisfied. The two TPMs are the translational 3-RUU and the DELTA robot. The kinematic analyses of these two TPMs are different from one another only when velocity and accelerations are considered. The result of this study is that the analytic expression of the surfaces bounding their workspace is a fourth degree polynomial equation, in the coordinates of a plattorm point, which contains all the manipulator geometric parameters. This analytic expression is given in an explicit form. The use of this expression is illustrated through a numerical example.

New dimensionally homogeneous jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators

Development of optimal design methods for parallel manipulators is important in obtaining an optimal architecture or pose for the best kinetostatic performance. The use of performance indexes such as the condition number of the conventional Jacobian matrix that is composed of nonhomogeneous physical units, however, may lack in physical significance. In order to avoid the unit inconsistency problem in the conventional Jacobian matrix, we present a new formulation of a dimensionally homogeneous Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points that are coplanar with the mobile platform joints. The condition number of the new Jacobian matrix is then used to design an optimal architecture or pose of parallel manipulators for the best dexterity. An illustrative design example with a six-degree-of-freedom Gough-Stewart platform parallel manipulator by using the proposed formulation is shown to generate the same optimal configurations as those from using the other existing dimensionally homogenous Jacobian formulation methods.

Orientation capability representation and application to manipulator analysis and synthesis

SummaryThis paper proposes a new orientation representation of planar manipulators by resorting to polar coordinates. Connecting the end-effector point to the first joint of a manipulator with a virtual adjustable link, the length of the adjustable link corresponds to a workspace point and is related to the orientation of the end effector link by a virtual angle in the form of a transcendental equation. Plotting this link length against the virtual angle in polar coordinates, the orientation of a manipulator can be represented in a compact form, and the range of partial dexterity can be identified. The characteristics of the new representation is hence revealed and related to the assessment of an orientation capability of a manipulator. Based on this representation, a desirable task can be presented and a manipulator can be synthesised with the required orientation.

Capturing of Moving Object and Ejecting with Grasp Type End Effector. 2nd Report. Dynamic Synthesis of a Shock Absorbing Mechanism.

This paper proposes a dynamic synthesis method of kinetic transmission mechanism between fingers and a DC motor in a shock absorbing end effector which yields no impulsive force responses in capture of moving object. In order to reduce equivalent values of inertial force and damping force at colliding point of end effector, singular point of mechanism is utilized by stretching wires between dual fingers. A desired velocity ratio of the transmission mechanism is derived from force equilibrium equations among tension of wires, inertial force and damping force of the DC motor. The Watt-type linkage is chosen as the transmission mechanism, and synthesized in order to satisfy above desired velocity ratio. Computer simulations are carried out to clarify the validity of the proposed mechanism at passive and active shock absorbing.

Capturing of Moving Object and Ejecting with Grasp Type End Effector. 1st Report. Proposal of Shock Absorbing Mechanism and Control Law.

This paper proposes a simple shock absorbing mechanism and stable capturing control law which makes no impulsive force responses in capture of a moving object. In order to reduce equivalent values of inertial force and damping force at colliding point of end effector, singular point of mechanism is utilized by stretching a wire between dual fingers. The passive shock absorbing performance is clarified by making comparison between the proposed mechanism and buffer materials. A desired active force which realizes stable positioning object at command position is calculated from estimated kinetic energy of the object. By inputting a desired value of tension transformed from the desired force to tension feedback control law, stable position control of the object is performed. On the other hand, for the sake of realizing accurate ejection velocity, a desired value of velocity control law is calculated from command velocity using a first lag system filter to reduce acceleration of the object at command velocity.

The Workspace of a General Geometry Planar Three-Degree-of-Freedom Platform-Type Manipulator

This paper focuses on the direct workspace problems of a general geometry fully-parallel-actuated, planar three-degree-of-freedom platform-type manipulator. A set of equations are presented that determine the workspace as a function of the platform orientation. The formulation is governed by the solution to the inverse position problem of the manipulator. The reachable positions of the end-effector point, for a specified platform orientation, are analyzed. To illustrate the concepts, a practical example is included where the end-effector is required to move a cup filled with water. Then the platform orientation, for a specified location of the end-effector point, is studied. If an arbitrary orientation is possible, the specified location of the end-effector point is said to be within the primary workspace. The paper includes a detailed discussion of the total primary workspaces of the manipulator. The approach adopted here is to regard the manipulator as a combination of three planar, three-revolute open chains. For the sake of completeness, the influence of special manipulator geometry on the workspace is also discussed. Finally, the paper includes the conditions that cause stationary configurations of the manipulator. Insight into these undesirable configurations is provided by a study of the location of the absolute instant center of the platform.

The End-Effector Angle and Manipulator Dexterous Workspaces

The end-effector angle is defined as the angle between the end-effector axial axis and the hand axis (an axis from the wrist center to the end-effector reference point). Most industrial manipulators posses a zero end-effector angle. This paper shows that the dexterity of a manipulator, which is indexed by the volume of dexterous workspace, is affected by the end-effector angle. Three 6-d.o.f., anthropomorphic manipulators and three types of dexterous workspace are used to study this influence. The results show that, for all three manipulators, the volume of a dexterous workspace in general increases along with the end-effector angle and it reaches maximum value when the end-effector angle is 90 deg. This influence is very obvious with the reachably dexterous workspace and the 180 deg spinnably dexterous workspace and is less obvious with the 360 deg spinnably dexterous workspace. These results somewhat confirm the fact that the majority of human hand prehensions used in daily life operations apply a nonzero end-effector angle.