A Unified Method for Computing Position and Orientation Workspaces of General Stewart Platforms

The workspace of a Stewart platform is a complex six-dimensional volume embedded in the Cartesian space defined by six pose parameters. Because of its large dimension and complex shape, such workspace is difficult to compute and represent, so that comprehension on its structure is being gained by studying its three-dimensional slices. While successful methods have been given to determine the constant-orientation slice, the computation and appropriate visualization of the constant-position slice (also known as the orientation workspace) has proved to be a challenging task. This paper presents a unified method for computing both of such slices, and any other ones defined by fixing three pose parameters, on general Stewart platforms involving mechanical limits on the active and passive joints. Additional advantages over previous methods include the ability to determine all connected components of the workspace, and any motion barriers present in its interior.

IRSBot-2: A Novel Two-DOF Parallel Robot for High-Speed Operations

This paper presents a novel two-degree-of-freedom (DOF) translational parallel robot for high-speed applications named the IRSBot-2 (acronym for IRCCyN Spatial Robot with 2 DOF). Unlike most two-DOF robots dedicated to planar translational motions, this robot has two spatial kinematic chains which confers a very good intrinsic stiffness. First, the robot architecture is described. Then, its actuation and constraint singularities are analyzed. Finally, the IRSBot-2 is compared to its two-DOF counterparts based on elastostatic performances.

A New Variable Stiffness Suspension Mechanism

A new variable stiffness suspension system based on a recent variable stiffness mechanism is proposed. The overall system is composed of the traditional passive suspension system augmented with a variable stiffness mechanism. The main idea is to improve suspension performance by varying stiffness in response to road disturbance. The system is analyzed using a quarter car model. The passive case shows much better performance in ride comfort over the tradition counterpart. Analysis of the invariant equation shows that the car body acceleration transfer function magnitude can be reduced at both the tire-hop and rattle space frequencies using the lever displacement transfer function thereby resulting in a better performance over the traditional passive suspension system. An H∞ controller is designed to correct for the performance degradation in the rattle space thereby providing the best trade-off between the ride comfort, suspension deflection and road holding.

A Coordinate-Free Approach to Tracing the Coupler Curves of Pin-Jointed Linkages

In general, high-order coupler curves of plane mechanisms cannot be properly traced by standard predictor-corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple coordinate-free method that first traces these curves in a distance space and then maps them onto the mechanism workspace is proposed. Tracing a coupler curve in the proposed distance space is much simpler because (a) the equation of this curve in this space can be straightforwardly obtained from a sequence of bilaterations; and (b) the curve in this space naturally decomposes into branches in which the signs of the oriented areas of the triangles involved in the aforementioned bilaterations remain constant. A surjective mapping permits to map the thus traced curves onto the workspace of the mechanism. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage, curves that can reach order 48.

Wrench Capability Analysis of Cable-Driven Parallel Mechanisms

The maximum wrench capabilities of the cable-driven parallel mechanisms are investigated in this paper. Focusing on accuracy and efficiency, two methods, an optimization-based method and a hybrid method based on optimization and geometry, are presented for determining the wrench capability of the cable-driven parallel mechanisms. Both methods are applied to a 6-DOF cable-driven parallel mechanism with eight cables to compute the maximum isotropic force and maximum isotropic moment. Comparison of the two methods is made. The results show that the hybrid method proposed is more accurate and computationally efficient.

Five Position Synthesis of a Slider-Crank Function Generator

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

Towards Parallel Cable-Driven Pantographs

We propose a new class of pantographs, i.e., of mechanisms that allow the reproduction of the displacements of an input link, the master, with an output link, the slave. The application we envision for these devices is the telemanipulation of objects from small distances, at low cost, where magnetic fields or other design constraints prohibit the use of electromechanical systems. Despite the long history of pantographs, which were invented in the 17th century, the class of pantographs proposed here is new, as it relies on parallel cable-driven mechanisms to transmit the motion. This allows the reproduction of rigid-body displacements, while previous pantographs were limited to point displacements. This important characteristic and others are described in the paper. One important challenge in the design of the proposed systems is that the cables must remain taut at all time. We address this issue by introducing nonlinear springs that passively maintain a minimum tension in the cables, while approximating static balancing of the mechanism over its workspace. Approximating static balancing allows the forces applied at the slave to reflect more accurately at the master, and vice versa. As a preliminary validation, a two-degree-of-freedom parallel cable-driven pantograph is designed. A prototype of this apparatus that does not include approximate static balancing is built, which demonstrates the working principle of these mechanisms.

Improved PID Control Using an Adaptive Two-Input Single-Output Coarse/Fine Approach

In robotic manufacturing, the qualities of responsiveness (speed) and accuracy are both desirable, but these two goals tend to oppose each other. A theoretical model of an adaptive PID controller for robotic and other actuated mechanical systems is presented here in pursuit of these combined objectives. Emphasis is placed on rotational velocity control using multiple inputs to produce a single desired output. Shared control of the system between two motors is proposed such that dominance of each motor controller shifts smoothly as a function of error signal based on the kinematic combination of the motor inputs (continuously sliding modes). Performance and stability analyses are provided to illustrate the behavior of the system based on operating parameters.

Development of a Control Method of a Walking Assistance Apparatus for the Elderly or Rehabilitants

A prototype for a walking assistance apparatus for the elderly or rehabilitants of motor palsy patients was developed as a next-generation vehicle or movable neuro-rehabilitation training appliance, using a novel spatial parallel link mechanism and a bearing lift. The flat steps of the apparatus move in parallel with the ground; the apparatus can support entire leg alignment (including soles) and assist; walking behavior at ankle, knee and hip joints simultaneously. To respond to the variation of equipped person’s walking velocity, the length of stride and walking cycle while walking with wearing the apparatus were compensated by using walking ratio. Therefore the apparatus can be controlled in response to equipped person’s will. Next, we developed a control method of the apparatus by using impedance control, taking into account the dynamics of the apparatus and the legs of an equipped person, and assist ratio for the equipped person. By adjusting the value of natural angular frequency of the desired dynamic equation for the equipped person, this apparatus can assist walking according to the equipped person’s desired response of the apparatus. Furthermore, motor palsy and muscle weakness patients can walk by themselves by using the apparatus; patients who have ambulation difficulty can use the apparatus with weight bearing lift that we developed. Using the apparatus with the weight bearing lift prevents stumbling and enables input of walking movement to the brain motor area. From the results of measured %MVC, the validity of the weight bearing lift was shown.

An XYZ Parallel Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.