Constraint Equations for a Planar Parallel Platform

<p>The aim of this thesis is to apply the Grünwald–Blaschke kinematic mapping to standard types of parallel general planar three-legged platforms in order to obtain the univariate polynomials which provide the solution of the forward kinematic problem. We rely on the method of Gröbner basis to reach these univariate polynomials. The Gröbner basis is determined from the constraint equations of the three legs of the platforms. The degrees of these polynomials are examined geometrically based on Bezout’s Theorem. The principle conclusion is that the univariate polynomials for the symmetric platforms under circular constraints are of degree six, which describe the maximum number of real solutions. The univariate polynomials for the symmetric platforms under linear constraints are of degree two, that describe the maximum number of real solutions.</p>

Constraint Equations for a Planar Parallel Platform

<p>The aim of this thesis is to apply the Grünwald–Blaschke kinematic mapping to standard types of parallel general planar three-legged platforms in order to obtain the univariate polynomials which provide the solution of the forward kinematic problem. We rely on the method of Gröbner basis to reach these univariate polynomials. The Gröbner basis is determined from the constraint equations of the three legs of the platforms. The degrees of these polynomials are examined geometrically based on Bezout’s Theorem. The principle conclusion is that the univariate polynomials for the symmetric platforms under circular constraints are of degree six, which describe the maximum number of real solutions. The univariate polynomials for the symmetric platforms under linear constraints are of degree two, that describe the maximum number of real solutions.</p>

Structure Synthesis and Reconfiguration Analysis of Variable-DOF Single-Loop Mechanisms With Prismatic Joints Using Dual Quaternions

This paper deals with the structure synthesis and reconfiguration analysis of variable-DOF (variable degree-of-freedom) single-loop mechanisms with prismatic joints based on a unified tool - the dual quaternion. According to motion polynomials over dual quaternions, an algebraic method is presented to synthesize variable-DOF single-loop 5R2P mechanisms (R and P denote revolute and prismatic joints respectively), which are composed of the Bennett and RPRP mechanisms. Using this approach, variable-DOF single-loop RRPRPRR and RRPRRPR mechanisms are constructed by joints obtained from the factorization of motion polynomials. Then reconfiguration analysis of these variable-DOF single-loop mechanisms is performed in light of the kinematic mapping and the prime decomposition. The results show that the variable-DOF 5R2P mechanisms have a 1-DOF spatial 5P2P motion mode and a 2-DOF Bennett-RPRP motion mode. Furthermore, the variable-DOF 5R2P mechanisms have two transition configurations, from which the mechanisms can switch among their two motion modes.

Design of Single-DOF Immersive Upper Limb Rehabilitation System via Kinematic Mapping and Virtual Reality

Mechanical devices such as robots are widely adopted for limb rehabilitation. Due to the variety of human body parameters, the rehabilitation motion for different patients usually has its individual pattern, thus we adopt clustering-based machine learning technique to find a limited number of motion patterns for upper-limb rehabilitation, so that they could represent the large amount of those from people who have various body parameters. Using the regression motion of the clustering result as the task motion, in this paper we seek to apply kinematic-mapping-based motion synthesis framework to design a one-DOF mechanism such that it could lead the patients’ upper limb through the task motion. Also,considering rehab training generally involves a large amount of repetition in daily basis, this paper has developed an immersive rehab system with Unity3D based on Virtual Reality (VR). A patient user interface as well as an administrator user interface are presented, and a two-mode rehabilitation strategy is proposed. The construction of the integrated system and a prototype of the upper limb rehab device are also shown in the end of this paper.

Design of Planar 1-DOF Cam-Linkages for Lower-Limb Rehabilitation Via Kinematic-Mapping Motion Synthesis Framework

When designing linkage mechanisms for motion synthesis, many examples have shown that the optimal kinematic constraint on the task motion contains too large deviation to be approximately viewed as a single rotational or translational pair. In this paper, we seek to adopt our previously established motion synthesis framework for the design of cam-linkages for a more accurate realization, while still maintaining a 1-degree-of-freedom (DOF) mechanism. To determine a feasible cam to lead through the task motion, first a kinematic constraint is identified such that a moving point on the given motion traces a curve that is algebraically closest to a circle or a line. This leads to a cam with low-harmonic contour curve that is simple and smooth to avoid the drawbacks of cam mechanisms. Additional constraints could also be imposed to specify the location and/or size of the cam linkages. An example of the design of a lower-limb rehabilitation device has been presented at the end of this paper to illustrate the feasibility of our approach. It is shown that our design could lead the user through a normal walking motion.

Novel approach for planetary gear train dimensional synthesis through kinematic mapping

The synthesis of a kinematic trajectory traversed by an output link (planet gear) and posture of a planetary gear train with noncircular gears can be divided into two phases: dimensional synthesis of the open-chain 2R mechanism (planetary carrier) and optimization of the transmission ratio of noncircular gear pairs. According to kinematic mapping theory, more than one closed coupler trajectory can be obtained by five preset poses. Simultaneous consideration of the trajectory shape, posture, and gear ratio is difficult during planetary gear train synthesis. This work therefore proposes a new method for the synthesis of planetary gear train in which different path segments in different trajectories are selected and a group of same-type 2R mechanisms is employed to pass through them in order to rebuild a new, closed trajectory. Subsequently, the transmission ratio of noncircular gear pairs can be determined using the relative angular displacement of the 2R mechanism. To improve the roundness of the pitch curves of noncircular gears, two optimization steps are implemented using a genetic algorithm without alternating the data points of the requisite open trajectories. For example, a mechanism for rice pot seedling transplanting is obtained by using the method.

Modeling the robotic manipulation of woven carbon fiber prepreg plies onto double curved molds: A path-dependent problem

This paper investigates the behavior of woven prepreg plies being placed on a weakly double curved mold by a robot. It is essential that the draped configuration is free from wrinkles. The baseline is a virtual draping environment that can plan and simulate robot draping sequences. It consists of a kinematic mapping algorithm for obtaining target points for the grippers on the mold surface. A simple motion planner is used to calculate the trajectories of the grippers. Here, two conceptually different draping strategies are employed. Finally, the two generated draping sequences are simulated using a transient, non-linear finite element model and compared w.r.t. their predicted wrinkle formations. Material data are obtained by means of tension, bias-extension and cantilever tests. The numerical examples show that the virtual draping environment can aid in developing the automatic draping system but that the generation of feasible draping sequences is highly path dependent and non-trivial.