In order to solve inverse kinematics of a multi-DOF (degree of freedom) mechanism, many methods have been proposed with the Jacobian linearization method. When solving inverse kinematics problems of the biped robot with this method, long computation time is required since the Jacobian matrix should be updated in order to solve the configuration for each different end-effector trajectory knot. I...

Parallel manipulators have separate serial kinematic chains that are linked to the ground and the moving platform at the same time. They have some potential advantages over serial robot manipulators such as high accuracy, greater load capacity, high mechanical rigidity, high velocity and acceleration (Kang et al., 2001; Kang & Mills, 2001). Planar Parallel Manipulators (PPMs), performing two tr...

This paper describes a new parallel robot with 6 degree of freedom (dof) and decoupled kinematics. The robot is composed of six legs with actuated prismatic joints; three legs control the spatial position of the center of the mobile platform, while the remaining legs are used to define the end effector orientation. The decouple kinematics is obtained by using a new approach for a triple spheric...

The inverse kinematics of a robot is the mapping that, given a goal position, calculates a set of joint positions so as to place the robot’s end effector in the specified goal. As this is a relevant issue to move the robot, there has been a lot of work about obtaining a fast and robust inverse kinematic algorithm. In this work we present the main concerns on finding an inverse kinematics algori...

This is the second part of a three-part paper. It extends to the free walking results of a previous work on postural equilibrium of a lower limb exoskeleton for rehabilitation exercises. A classical approach has been adopted to design gait (zero moment point (ZMP), linearized inverted pendulum theory, inverse kinematics obtained through the pseudo-inverse of Jacobian matrices). While several id...

The inverse kinematics problems of redundant manipulators have been investigated for many years. The conventional method of solving this problem analytically is by applying the Jacobian Pseudoinverse Algorithm. It is effective and able to resolve the redundancy for additional constraints. However, its demand for computational effort makes it not suitable for real-time control. Recently, neural ...

This paper presents a two degree-of-freedom (DOF) planar parallel manipulator with two linear actuators, whose degree of freedom is dependent on a passive constraining leg connecting the base and the platform. The kinematics of the presented manipulator is first studied: the inverse and forward kinematics problems are solved in the closed form, the practical workspace is described symbolically,...

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The man...

In the literature we find a variety of mathematical approaches for solving problems in robotics which we will review now briefly. Denavit and Hartenberg [60] introduced the mostly used kinematic notation for lower pair mechanisms based on matrix algebra, Walker [243] used the epsilon algebra for the treatment of the manipulator kinematics, Gu and Luh [99] utilized dual– matrices for computing t...