Serial Chain Mechanisms Research Articles

An Integrated Kinematic Mapping and Fourier Method to Design Spherical Coupled Serial Chain Mechanisms for Single-Joint Rehabilitation

Abstract Robotic devices are capable of reducing the physical burden on rehabilitation therapists and providing training programs of good repeatability, high efficiency, and high precision. When designing the kinematic structure for rehabilitation robots, there has been a growing interest toward one-degree-of-freedom (DOF) end-effector mechanisms due to their simpler structure and less complicated control algorithms. Compared with current one-DOF mechanism designs that are mainly customized for multi-joint robotic training, spherical coupled serial chain (SCSC) mechanisms are proposed in this paper to specifically deliver the single-joint robotic training, which is of equal importance to the effective physical recovery. Using kinematic mapping theory, the end-effector motion of SCSC mechanisms can be naturally transformed to two trigonometric curves composed of finite Fourier series in two separate planes of the image space. This novel formulation helps to establish an analytical and direct relationship between the design parameters of the SCSC mechanism and the harmonic parameters of the image-space representation of the task rehabilitation motion. The result is a simple and effective method for kinematic synthesis of SCSC mechanisms for generation of single-joint motion with an arbitrary number of spherical poses. An example of designing SCSC mechanisms for shoulder-joint rehabilitation is presented at the end of this paper to illustrate the feasibility of the proposed method.

Effective Tool-Point Acceleration of Serial Chain Mechanisms Based on Basic Geometric Transformations

In this paper, a method to manage the actuator parameters of a serial chain mechanism composed of revolute joints to achieve improved responsiveness characteristics (acceleration capability) based on the basic geometric parameters of the mechanism is presented. Here, an analytic framework presented by the authors in an earlier work, which exploits the geometric structure of this type of mechanism is extended to address the tool-point mass and acceleration. The manipulator’s geometry is reduced to a set of lengths, which are representative of the mechanical gains associated with the manipulator and they, along with the transmission ratio of the actuators, are used to map the actuator parameters to their effective values at the tool-point where a direct comparison to the task requirements can be made. With this method, minimal computations are required to evaluate the system’s performance since only the forward kinematic computations are required. The effects of the actuator transmission ratio parameter on the effective tool-point force, mass, and acceleration are investigated for a six-DOF serial chain manipulator. Through this case study, it is demonstrated how the transmission ratio is managed to balance the system’s effective tool-point force and mass to obtain an optimal tool-point acceleration. In addition to the investigation of the effects of the actuator parameters, the method is shown to be useful in the solution of the configuration management or modular design problem since the exponential design space can be searched for a globally optimal solution with minimal computations. The goal of the configuration management problem is to quickly configure and/or reconfigure a robotic manipulator from a finite set of actuator modules.

Design Criteria for Serial Chain Mechanisms Based on Kinetic Energy Ratios

In this article, a description of the kinetic energy partition values (KEPVs) of serial chain mechanisms, as well as their rates of change, is presented. The KEPVs arise from the partitioning of the mechanism’s kinetic energy and correspond to the critical values of the kinetic energy ratios of the actuators and links and are indicators of the kinetic energy distribution within the system while the rates of change in the KEPVs indicate the sensitivity to change in the location of that kinetic energy. A high value for the KEPV rate of change together with a high operational state implies that the amount of kinetic energy flowing in the system is large, further implying a loss of precision in the system due to large inertial torques being generated. The KEPVs and their rates can be used to identify the actuators whose parameters (mass, inertia, and mechanical gain) greatly affect the overall distribution of kinetic energy within the system, thereby allowing the designer to optimize these actuators to improve the performance of the overall mechanism. Two design criteria, one based on the KEPVs and another based on their rates of change, are developed. A two degree-of-freedom (DOF) planar mechanism is used to demonstrate the concepts and to verify the properties of the KEPVs and their rates. Also, a 6DOF spatial manipulator is used to illustrate the solution of a multicriteria design optimization problem where two conflicting criteria are considered: a KEPV criterion and an effective mass criterion. The goal of the design problem is to demonstrate how the inertial parameters of the actuators and the mechanical gains of the actuator transmissions alter the kinetic energy of the system both in terms of its magnitude, which is “measured” via the effective mass criterion, and its distribution, which is measured via the KEPV criterion. It is demonstrated that the mechanical gains in the actuators significantly influence the magnitude of the kinetic energy as well as its distribution within the system due to the inertial amplification. The KEPVs and their rates of change provide a novel new approach to analyzing the dynamic character of serial chain mechanisms.

Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms

Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class of mechanisms that can be realized by coupling successive joint rotations of a serial chain linkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits of single degree-of-freedom design and control with the anthropomorphic workspace of serial chains. Our interest is in creating articulated manipulation-assistive aids based on the SDCSC configuration to work passively in cooperation with the human operator or to serve as a low-cost automation solution. However, as single-degree-of-freedom systems, such SDCSC-configuration manipulators need to be designed specific to a given task. In this paper, we investigate the development of a synthesis scheme, leveraging tools from Fourier analysis and optimization, to permit the end-effectors of such manipulators to closely approximate desired closed planar paths. In particular, we note that the forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. The proposed Fourier-based synthesis method exploits this special structure to achieve the combined number and dimensional synthesis of SDCSC-configuration manipulators for closed-loop planar path-following tasks. Representative examples illustrate the application of this method for tracing candidate square and rectangular paths. Emphasis is also placed on conversion of computational results into physically realizable mechanism designs.

Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms

Single Degree-of-freedom Coupled Serial Chain (SDCSC) mechanisms form a novel class of modular and compact mechanisms with a single degree-of-freedom, suitable for a number of manipulation tasks. Such SDCSC mechanisms take advantage of the hardware constraints between the articulations of a serial-chain linkage, created using gear-trains or belt/pulley drives, to guide the end-effector motions and forces. In this paper, we examine the dimensional synthesis of such SDCSC mechanisms to perform desired planar manipulation tasks, taking into account task specifications on both end-effector motions and forces. Our solution approach combines precision point synthesis with optimization to realize optimal mechanisms, which satisfy the design specifications exactly at the selected precision points and approximate them in the least-squares sense elsewhere along a specified trajectory. The designed mechanisms can guide a rigid body through several positions while supporting arbitrarily specified external loads. Furthermore, torsional springs are added at the joints to reduce the overall actuation requirements and to enhance the task performance. Examples from the kinematic and the kinetostatic synthesis of planar SDCSC mechanisms are presented to highlight the benefits.

Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms

The dimensional synthesis of a spatial two revolute jointed dyad for path following tasks with applications to coupled serial chain mechanisms is presented. The precision point synthesis equations obtained using the rotation matrix approach form a rank-deficient linear system in the link-vector components. The nullspace of this rank-deficient linear system is derived analytically and interpreted geometrically. The nullspace vectors lead to the specification of additional constraints via the so-called auxiliary equations and to the solution of the linear system of equations. The geometry also allows the derivation of a closed form solution for the three design position problem. Finally, optimal path following by coupled R-R dyads is achieved by optimization over the free choice variables.

Robust Joint and Cartesian Control of Underactuated Manipulators

Underactuated manipulators are robot manipulators composed of both active and passive joints in serial chain mechanisms. The study of underactuation is significant for the control of a variety of rigid-body systems, such as free-floating robots in space and gymnasts, whose structure include passive joints. For mechanisms with large degrees of freedom, such as hyper-redundant snake-like robots and multi-legged machines, the underactuated structure allows a more compact design, weight decrease, and energy saving. Furthermore, when one or more joints of a standard manipulator fail, it becomes an underactuated mechanism; a control technique for such system will increase the reliability and fault-tolerance of current and future robots. The goal of this study is to present a robust control method for the control of underactuated manipulators subject to modeling errors and disturbances. Because an accurate modelling of the underactuated system is more critical for control issues than it is for standard manipulators, this method is significant in practice. Variable structure controllers are proposed in both joint space and Cartesian space, and a comprehensive simulation study is presented to address issues such as computation, robustness, and feasibility of the methods. Experimental results demonstrate the actual applicability of the proposed methods in a real two-degrees-of-freedom underactuated manipulator. As it will be shown, the proposed variable structure controller provides robustness againstboth disturbances and parametric uncertainties, a characteristic not present on previously proposed PID-based schemes.