Forward Kinematic Transformation Research Articles

Planar and spherical four-bar linkage [formula omitted] algebraic input–output equations

The algebraic polynomial input–output (IO) equations relating any two of the relative joint displacement parameters, called vi and vj, between any of the six distinct pairs of rigid links in arbitrary planar and spherical four-bar mechanisms are derived. First, the forward kinematics transformation matrices of the corresponding serial kinematic chains are computed in terms of their Denavit–Hartenberg parameters, but with all angles converted to tangent half-angle parameters. These matrices are mapped to their corresponding Study soma coordinates. The serial kinematic chain is closed by equating the soma coordinates to the identity array. Algebraic polynomial elimination methods are then used to obtain a single polynomial in terms of only the design and the selected IO joint displacement parameters. This yields six independent algebraic IO Equations for each of the planar and spherical 4R linkages; the same techniques are applied to derive six additional algebraic IO equations for each of the RRRP and PRRP planar linkages providing a catalogue of 24. The utility of these IO equation sets is demonstrated via discussion of the associated mobility and design parameter spaces.

A New 2T-2R Hybrid Parallel Manipulator

Though computer technology has brought about virtual manufacturing to expedite design and analysis through simulation and visualization, machines remain essential, as ultimately products need to be made. There is a need for equipment providing more than three degrees of freedom (DOF) arranged in parallel and based on simpler arrangements than 6-DOF arrangements in application. This paper presents a new 4-DOF hybrid parallel platform manipulator with fixed-leg lengths and base mounted prismatic actuators. The movable platform of the manipulator can translate along two directions and rotate around two axes respectively (2T-2R). The kinematics model is formulated, which describes the inverse and forward kinematics transformation. It is very easy to develop a 5-axis NC machine-tool which is of large-workspace based on the 2T-2R, 4-DOF parallel mechanism presented in this paper.

A Four Degrees of Freedom Parallel Manipulator for Machining

In the past decades, a number of parallel manipulators have been extensively studied. However, most efforts are dedicated to six degrees of freedom (DOF) or three-DOF manipulators. There is a need for equipment providing more than three DOF's arranged in parallel and based on simpler arrangements than six-DOF arrangements in application. This paper presents a novel four-DOF parallel platform manipulator with base mounted prismatic actuators. The manipulator is driven by four linear actuators. The movable platform of the manipulator can translate along two directions and rotate around two axes respectively. The kinematics model is formulated, which describes the inverse and forward kinematics transformation. It is very easy to develop a five-axis NC machine-tool which is of large-workspace based on the four-DOF parallel mechanism presented in this paper.

Exact methods for determining the kinematics of a stewart platform using additional displacement sensors

AbstractThe Stewart platform (SP) is a parallel closed‐kinematic chain robotic mechanism that is capable of providing high structural and positional rigidity. Because of its unique capability, the platforms have been employed in many control engineering applications such as simulator shakers, robotic manipulators, etc. However, a main problem often found in the implementation of a real‐time controller for the platform is the lack of an efficient algorithm for solving its highly nonlinear forward kinematic transformation (FKT), where one seeks to find the translational and orientational altitudes of the moveable platform from knowing the lengths of the platform linkages. This article describes two new direct and exact methods for computing the translational and rotational displacements of an SP by employing extra transnational displacement sensors (TDSs), in addition to the existing TDSs for the six links of the SP. The key for the approach lies in knowing where to employ the TDSs for determining positional vectors of strategic platform locations. By taking advantage of a tetrahedral geometry, closed‐form solutions for the FKT can then be derived and directly evaluated. The new methods produce accurate solutions with only minimal computation necessary. The advantages and disadvantages of the proposed methods are discussed and compared to an existing method. The exact methods are being investigated for an on‐line implementation of a nonlinear adaptive control system and redundancy scheme for a 25‐ton Stewart platform‐based Crew Station/Turret Motion Base Simulator (CS/TMBS) at the U.S. Army Tank‐Automotive Command (TACOM).

Trajectory planning and control of a Stewart platform-based end-effector with passive compliance for part assembly

This paper presents the kinematic analysis and trajectory planning for a six-degrees-of-freedom end-effector whose design is based on the Stewart platform mechanism. The end-effector is composed of two platforms and six linear actuators driven by stepper motors. A spring-loaded platform is used to provide passive compliance to the end-effector during a part assembly. A closed-form solution is derived for the inverse kinematic transformation and a computationally effective numerical solution is obtained for the forward kinematic transformation using the Newton-Raphson method. Three trajectory planning schemes, two for fine motion and one for gross motion are developed. Experimental results of tracking various test paths are presented.

Analysis and control of a kinematically redundant manipulator

To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having 7 degrees-of-freedom and a master hand controller system. This paper presents the mathematical developments required for the computer simulation study and motion control of the slave arms. First the slave arm forward kinematic transformation is derived using the Denavit-Hartenberg notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternion representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. Finally three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector and some preliminary results of the proposed control schemes are presented and discussed.

Automatic generation of forward and inverse kinematics for a reconfigurable modular manipulator system

AbstractTraditional industrial and research manipulators have a fixed configuration and are thus suited for a certain class of tasks. In order to make manipulators flexible and suited for a larger class of tasks we have proposed the concept of a Reconfigurable Modular Manipulator System (RMMS). The RMMS consists of a set of modular links and joints of various sizes; reconfigurable manipulators are designed and built from this system as appropriate for a given task. In order to effectively utilize such a system, one needs algorithms for automatically generating the kinematic descriptions for an arbitrary manipulator configured from the RMMS. Previous research on the kinematics of robotic manipulators has addressed fixed configuration manipulator systems. In this article, we propose an algorithm for automatically generating both the forward and inverse kinematics of a serial link N degrees‐of‐freedom reconfigurable manipulator. Generation of the kinematic equations that govern a modular manipulator starts with geometric descriptions of the units, or modules, as well as their sequence in the manipulator. Using this geometric information, we determine the Denavit‐Hartenberg parameters of a reconfigurable manipulator. The Denavit‐Hartenberg kinematic parameters are then used to obtain the forward kinematic transformation of the system. We also address the problem of otaining the inverse kinematics of reconfigurable manipulators. In order to automate the inverse kinematics and to make the procedure as general as possible, we have proposed the idea of scaling a manipulator. We use the efficient numerical approach and in the case of a redundant manipulator, we exploit the extra degrees of freedom to achieve singularity avoidance. We have implemented our algorithms on an Ironies 68020 based single board computer that is used to control the prototype Reconfigurable Modular Manipular System (RMMS) which is being developed in our laboratory.