Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

A three degree of freed parallel micromanipulator is presented.The DOF of parallel manipulator is analyzed by the screw theory, the driven number is gotten. The kinematics solutions are analyzed using the vector theory, as a result, the velocity of a movable platform are derived. Based on Jacobian matrix, the forward and inverse kinematic singular configuration of the parallel micromanipulator is also studied. The results show that sensitivity parameters existed in Jacobian matrix affect the relation between the input and the output of the micromanipulator, the vector space method is simple and convenient in analyzing the singularity of parallel mechanisms. The simulation results verified that the robot has the tiny displace, and the kinematics parameters of the robot can be conveniently acquired, so the study provides theoretical bases for the robot control and performance improvement.

Adaptive control of parallel robots with uncertain kinematics and dynamics

This research presents a new spatial Parallel Manipulator (PM) with pure translational motion in a plane or 2-DOF PM for pickand-place operation. This spatial 2-DOF PM is constructed by the 2(RRR)-2(PRRR) kinematic chain and is named Ψ2. This Ψ2 PM offers simplicity in its architecture because each limb applies a 1- DOF joint. The applicability of Ψ2 for pick-and-place operations was investigated by performing kinematic and singularity analyses at the preliminary stage. The singularity of Ψ2 was determined by relying on its Jacobian matrices, where three kinds of singularity can be evaluated. Next, the singularity and Jacobian matrix hold a key to identifying the workspace in a regular geometrical shape required for the operation of such an application. The identified operational workspace must be free of singularity and good conditioning workspace. In this study, two predetermined values of Ψ2 kinematic parameters were used to evaluate the kinematic characteristics and singularity of the manipulator as well as to identify its operational workspace. According to the results, Ψ2 has a good prospect of being applied to high-speed pick-and-place operations.

The main concern of this paper is modeling and control of a cable-suspended parallel robot. Alongside lots of benefits, a major open issue in the design of these robots is ensuring tensile cable forces for any admissible motion. The latter problem is particularly challenging when under-constrained configurations are considered. In this paper kinematics, statics and dynamics model of the cable-suspended parallel robot is introduced in a general form. Towards ensuring positive and bounded cable tensions in under-constrained robot Fmincon function of Matlab is used. The proposed method, uses cables tension limits and Jacobian matrix. The controller take benefits from computed torque method which is powerful method for dynamic models. The method is explained and the results achieved prove that the proposed method may a priori ensure positive and bounded cable tensions along desired path.

The parallel manipulators with n<6 spherical joint-prismatic joint-spherical joint (SPS) type active legs and one passive constrained leg have attracted more attention and been used in many practical applications. This kind of parallel manipulator has a larger capability of load bearing and a simple structure of active leg. The paper used 4-SPS/PS four degree-of-freedom (DOF) parallel manipulator for the simulation of ship's heave and swing motion. Mobility property of the 4-SPS/PS parallel manipulator is analyzed by screw theory. The inverse position kinematics model is established and the analytical solution is obtained. It uses extra sensor and Sylvester resultant elimination to derive analytical solutions of forward position kinematics including two real solutions and two imaginary solutions, and uses vector cross product to derive the Jacobian matrix of 4-SPS/PS parallel manipulator. Furthermore, it introduces three performance indicators to analyze the singularity. In order to obtain accurate analysis results of singularity, it calculates the minimum singular value, condition number and manipulability degree of Jacobian matrix for different combination of pose, respectively.

Singularity analysis is one of the basic problems for parallel manipulators. When a manipulator moves in a singular configuration, the motion and transmission performance are poor. In certain serious cases, the normal operation could be damaged. Based on the topology structure and kinematics analysis of a 2(3HUS+S) parallel manipulator, the Jacobian matrices were established. Then, the singular locus surface was obtained by numerical simulation. In addition, the relationship between the motion path curve and the singular locus surface was analyzed. In this study, α, β, and γ are the attitude angles that describe the motion of moving platforms. There is a nonsingular attitude space in singular locus surfaces, and the singular locus surface is a single surface in a small attitude angle range. The nonsingular attitude space increases as the absolute value of γ increases, and singularity could be avoided when γ is large. Furthermore, the motion path curve passes through the singular locus surface two times, and the two intersection points are consistent with the positions where the motion dexterity is equal to zero. This study provides new insights on the singularity analysis of parallel manipulators, particularly for the structure parameter optimization of the nonsingular attitude space.

This paper focuses on the systematic type synthesis of parallel robot manipulators by using new structural formulas based on the screw theory. New structural formulas as a total number of screw in kinematic pairs , number of screws with variable pitch , total number of screws that represent the contact geometry of lower and higher joint elements (t), mobility equation for robot manipulators (M), dimension of the closed loop , motion of end effector of parallel manipulator , number degree of freedom of kinematic pairs , refers to find the kinematic structure of robot manipulators realizing a specified motion requirement. Twenty kinematic pairs with structural parameters are introduced. History of six structural formulas using for structural synthesis of parallel robot manipulators from space and different subspaces are presented as a table with equations, authors, years and some commentaries. The structural synthesis approach is based on the elementary notions of screw theory. Using the proposed of structural formulas approach, families of platform manipulators are constructed from a set of structural units. This paper is appropriate for engineers with interest in robotics, rovers, space docking parallel manipulators and screw theory.

We report the control and simulation of a planar cable-driven parallel robot with four cables. The application of the robot is to fully control the lower limb, shank, for gait rehabilitation. The main challenge in control of the cable-driven parallel robot is to avoid negative cable tensions during dynamic motions. For this purpose a redundant robot with capability to exert a general wrench on the target limb with only positive cable tensions for all the poses of the limb near to the trajectory in the gait cycle is used. It is explained that the proposed robot can control both rotational and translational degree of freedom of the shank without slack cable conditions in the gait cycle. Then the dynamic model and control of the robot is proposed with a strategy to choose the forces of cables in order to avoid the negative tension. Examples of simulation are presented to demonstrate the capability of the robot in efficiently tracking the trajectory.

The kinematic and dynamic analysis of the high-degree of freedom (dof) hybrid systems that using serial and parallel robots together on fixed or mobile platform such as legged robots and service robots, is a rather difficult and complex, time consuming problem and a topic of great interest for researchers. There are many educational and commercial toolboxes which analyze serial and parallel robots separately. With the toolbox developed here, high-dof serial, parallel and hybrid robotics systems used on both fixed and mobile platforms can be designed and studied easily. Forward and inverse kinematics, Jacobian matrix, singularities, trajectory planning, torques and forces in joint and operational space can be examined with different robot designs. Using the toolbox that proposed in this paper, robot designer, researchers, students and educators can easily develop their own robotics systems and visualize them in the virtual reality environment provided by MATLAB. Also, it helps understanding fundamentals of high-dof multi-body hybrid robotics systems through user friendly interactive simulation. The most of existing toolboxes in the literature allow only user to analyze the predefined robots in their library with limited interactive capabilities. In some of them, the user can define a new robot with limited dof. But, the user must already have a prior knowledge about designing process of robots. In the proposed toolbox, designing and defining any new robotics systems become very easy. What makes this toolbox unique compared with the existing toolboxes is that any type of robot structures with high dof can be developed, analyzed and studied in detail.

The research explores the design and fabrication of a cable-driven parallel robot (CDPR) as an innovative and alternative method for in-situ robotic construction. CDPRs consist of a mobile platform attached to a fixed frame by several cables that are controlled through actuating winches. Their increased mobility reveals an immense potential for in-situ design-fabrication solutions emphasizing the importance of local materials and local economies. The paper presents a facet of this research focusing on the development of a novel design tool for the control and simulation of cable-suspended parallel robots in order to facilitate architectural design-fabrication explorations while addressing the complexities associated with parallel robots.

The paper presents design and control simulations of ISOGLIDE3 parallel robot. An innovative user interface for high-level control of a 3 DOF parallel robot is also pre-sented. The robot interface using virtual reality was veri-fied and tested, and results in MATLAB, Simulink, and SimMechanics were presented. The ISOGLIDE3 robot offers the superior characteristics with regards to the other parallel manipulators, such as the light weight construc-tion. The presented 3 DOF parallel robot can be used for surgery due to its overall precision, good dynamic behav-ior.

Design and locomotion analysis of a novel modular rolling robot

This paper presents kinematic analysis of a 3-axis parallel manipulator, called P3. The P3 parallel manipulator is developed based on a 3-PRRU parallel mechanism, where P denotes prismatic pair, R revolute pair, and U universal joint. The P3 parallel manipulator can undergo two rotations and one translation without parasitic motion. First, a brief description of the P3 is presented. Then, forward and inverse kinematic solutions of the P3 are derived. Parasitic motion is discussed. The Jacobian matrix is obtained based on the velocity equations. Further, singular configurations of the P3 are identified. A special configuration where the actuation fails is also detected based on screw theory. The workspace of P3 is investigated.

In this paper, singular configurations of a new spatial rotation 4-SPS-1-S parallel manipulator are examined. The 4-SPS-S parallel manipulator has 3 purely rotational degrees of freedom in the space, and can perform spatial roll, pitch and yaw rotation motions. It possesses high load capacity, stiffness and stability. Inverse position analysis and velocity mapping equations of the mechanism are presented, and then Jacobian matrices are built. Transformation from output velocity to input velocity is explored and computed. The square root of determinant of J <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> J matrix is adopted as an actuating performance index, serving as a criteria to judge singularities of the mechanism. A numerical example is presented to illustrate the distribution of actuating performance indexes across the workspace followed by singularity analysis. The paper provides crucial information for the design of this type of parallel manipulator.

In this paper, simulation, kinematics analysis, and control of a 3-DOF Delta parallel robot have been investigated. Delta parallel robots are one of the most popular manipulators for industrial applications. The kinematic equations of the robot have been established by the screw theory, in which, the position and velocity analyses have been carried out. In SimScape simulation environment, the kinematic model of the robot has been verified and subsequently, an inverse kinematic model was adopted for control purposes. In order to improve the tracking ability of the robot, three important control approaches, consisting in PID, adaptive control, and a Sliding Mode Control (SMC) have been implemented. Afterwards, the effectiveness of each approach has been investigated by employing the root mean square error (RMSE) index. By comparing the obtained index values, the SMC demonstrates the best performance with the RMSE value of 0.4188 in comparison to other methods. Simulation results were illustrated to show the ability of the controllers to reject white noise disturbance added to the system's input signals.