Kinematic and dynamic analysis of a spatial one-DOF foldable tensegrity mechanism

This paper presents a mechanical analysis of a spatial 1-DOF tensegrity mechanism created by connecting three planar tensegrity mechanisms to form a triangular prism. The subsequent investigation produced kinematic and dynamic models that allow the workspace-boundary singularities and minimum energy configuration to be determined. Singularities were found to occur when the mechanism is folded in the vertical X, Y plane or in the horizontal X, Z plane. The minimum energy configuration, formed by the angle between the horizontal plane and the actuated strut, was found to be θ= π/4. However, when the system was linearized to determine the analytic solution for the dynamics, the minimum energy configuration become θ = 1 due to the inherent error produced by the system linearization. The dynamic response of the mechanism to an initial small displacement was determined for each case of critically damped, overdamped, and underdamped systems

Reciprocating excitation of a flexible beam: Benchmark study

A long and slender flexible beam is set in oscillatory motion to observe its deflection. A novel application of digital image processing is employed to obtain contactless discrete measurements of the beam tip deflection. We compare the measured data to those predicted by a flexible multibody dynamics simulation (flxdyn). This study is intended as a benchmark. Moreover, the system is described in sufficient detail to enable other investigators to repeat, and build upon results herein presented for the first time

Continuous approximate synthesis of planar function-generators minimising the design error

It has been observed in the literature that as the cardinality of the prescribed discrete input-output data set increases, the corresponding four-bar linkages that minimise the Euclidean norm of the design and structural errors tend to converge to the same linkage. The important implication is that minimising the Euclidean norm, or any p-norm, of the structural error, which leads to a nonlinear least-squares problem requiring iterative solutions, can be accomplished implicitly by minimising that of the design error, which leads to a linear least-squares problem that can be solved directly. Apropos, the goal of this paper is to take the first step towards proving that as the cardinality of the data set tends towards infinity the observation is indeed true. In this paper we will integrate the synthesis equations in the range between minimum and maximum input values, thereby reposing the discrete approximate synthesis problem as a continuous one. Moreover, we will prove that a lower bound of the Euclidean norm, and indeed of any p-norm, of the design error for planar RRRR function-generating linkages exists and is attained with continuous approximate synthesis

Quadric Surface Fitting Applications to Approximate Dimensional Synthesis

An approximate synthesis method is pre- sented that takes a given set of n desired poses of the cou- pler of a four-bar planar mechanism and finds the “best” mechanism that can achieve them. This is accomplished by solving an equivalent unconstrained non-linear minimiza- tion problem. The hyperboloids of one sheet or hyperbolic paraboloids that minimize the distance between the given n poses in the kinematic mapping image space and n cor- responding points that belong to the quadric surfaces, rep- resent the “best” mechanism that can achieve the desired poses. The procedure is tested successfully on an RRRR mechanism

Self-Motions of General 3-RPR Planar Parallel Robots

This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the expressions for the singularity loci of 3-RPR planar parallel robots are determined. Then, the global behaviour at all singularities is geometrically described by studying the degeneracy of the direct kinematic model. Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted. Finally, a practical example is discussed and experimental validations performed on an actual robot prototype are presented

Dynamics and vibration analysis of the interface between a non-rigid sphere and omnidirectional wheel actuators

This paper presents analysis of the dynamics and vibration of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The purpose of the analysis is to serve as a design tool for the construction of a six-degree-of-freedom motion platform with unlimited rotational motion. The equations of motion are presented taking flexibility of the system into account. The behaviour of the system is illustrated by sample configurations with a range of omnidirectional wheel types and geometries. Vibration analysis follows, and

Atlas motion platform generalized kinematic model: Atlas motion platform

Conventional training simulators commonly use a hexapod configuration to provide motion cues. While widely used, studies have shown that hexapods are incapable of producing the range of motion required to achieve high fidelity simulation required in many applications. A novel alternative is the Atlas motion platform. This paper presents a new generalized kinematic model of the platform which can be applied to any spherical platform actuated by three omnidirectional wheels. In addition, conditions for slip-free and singularity-free motions are identified. Two illustrative examples are given for different omnidirectional wheel configurations

Pareto Optimality and Multiobjective Trajectory Planning for a 7-DOF Redundant Manipulator

This paper presents a novel approach to solve multiobjective robotic trajectory planning problems. It proposes to find the Pareto optimal set, rather than a single solution usually obtained through scalarization, e.g., weighting the objective functions. Using the trajectory planning problem for a redundant manipulator as part of a captive trajectory simulation system, the general discrete dynamic programming (DDP) approximation method presented in our previous work is shown to be a promising approach to obtain a close representation of the Pareto optimal set.When compared with the set obtained by varying the weights, the results confirm that the DDP approximation method can find approximate Pareto objective vectors, where the weighting method fails, and can generally provide a closer representation of the actual Pareto optimal set

A 3D scanning system for biomedical purposes

The use of three-dimensional (3D) scanning systems for acquiring the external shape features of biological objects has recently been gaining popularity in the biomedical field. A simple, low cost, 3D scanning syste

A discrete dynamic programming approximation to the multiobjective deterministic finite horizon optimal control problem

This paper addresses the problem of finding an approximation to the minimal element set of the objective space for the class of multiobjective deterministic finite horizon optimal control problems. The objective space is assumed to be partially ordered by a pointed convex cone containing the origin. The approximation procedure consists of a two-step discretization in time and state space. Following the first-order time discretization, the dynamic programming principle is used to find the multiobjective discrete dynamic programming equation equivalent to the resulting discrete multiobjective optimal control problem. The multiobjective discrete dynamic programming equation is finally discretized in the state space. The convergence of the approximation for both discretization steps is discussed