Gökhan Kiper

Deployable space structures

Deployable structures are mobile assemblies which do not aim motion but to attain different configurations depending on the service requirements. These structures are widely used in space applications due to storage limitations of the launch vehicles. The large diversity of design alternatives should be evaluated in design of deployable parts of spacecrafts. This study aims to present design alternatives of antennas, masts and solar panels of space devices. Also use of spatial linkages in deployable structure designs is discussed.

Fulleroid-Like Linkages

The Fulleroid, discovered by K. Wohlhart, is a 48-link overconstrained spatial linkage which expands and contracts within a rhombic dodecahedral boundary. In this paper, some similar types of linkages are synthesized based on some observations on the Fulleroid. First an infinite class of 24-faced polyhedral linkages is described. Next the idea is generalized for polyhedra having rhombic faces. Then analyzing these linkages a basic closed chain is derived as a module and some dipyramidal and stellated polyhedral linkages are synthesized using this module.

Regular Polygonal and Regular Spherical Polyhedral Linkages Comprising Bennett Loops

In this study, assemblies of Bennett loops constructing regular polygonal linkages and regular polyhedral linkages are presented. The regular polyhedral linkages, necessarily, depend on spherical polyhedral shapes. Most of the resulting linkages have single degree of freedom, but there are exceptions such as a cubic linkage.

Position Kinematics of a 3-RRS Parallel Manipulator

The 3-RRS parallel manipulator presented in this study comprises of parallel revolute joint axes in each leg. The manipulator is composed of a base and a moving platform which are in the shape of equilateral triangles. Moving platform has two rotational and one translational degrees-of-freedom. This study formulates the forward and inverse kinematics of the parallel manipulator. A 16\(^{th}\) order polynomial in terms of one of the passive joint variables is obtained for the forward kinematic analysis. Numerical results and the corresponding pose of the manipulator for inverse and forward kinematics are presented.

Derivation of Input/Output Relationships for the Bennett 6R Linkages Based on the Method of Decomposition

The Bennett overconstrained 6R linkages are the double-planar, the double-spherical and the plano-spherical 6R linkages. These mechanisms are obtained by combining simple planar and/or spherical mechanisms and then removing one of the common links. This paper presents the derivation of the input/output relationships for these mechanisms using the decomposition method. This method is based on writing the input/output equations for the two imaginary loops comprising the 6R mechanism and then eliminating the imaginary joint variable. It is found that the resulting input/output equations contain up to 4th power of trigonometric terms, such as cos4 θ.

Some Properties of Jitterbug-Like Polyhedral Linkages

A formal definition for Jitterbug-like polyhedral linkages is presented. It is shown that the supporting polyhedral shapes cannot be arbitrary and some topological properties are derived. Also it is demonstrated that the link lengths of the spatial loops comprising the linkage cannot be arbitrary. The spherical indicatrices of spatial loops are examined and are shown to be immobile.

Kinematic Design of a Reconfigurable Deployable Canopy

A reconfigurable and deployable mechanism is proposed for a canopy which can also be used as a tent or a semi-open structure. The proposed single degree-of-freedom mechanism has four assembly modes. The conditions for deployment and reconfiguration of the mechanism are derived. These conditions impose three equality and two inequality constraints on the 11 design parameters of the mechanism. A virtual model of the mechanism is constructed in Excel for design and simulation purposes. A computational case study is presented.

Function Generation Synthesis with a 2-DoF Overconstrained Double-Spherical 7R Mechanism Using the Method of Decomposition and Least Squares Approximation

This study addresses the approximate function generation synthesis with an overconstrained two degrees-of-freedom double spherical 7R mechanism using least squares approximation with equal spacing of the design points on the input domain. The 7R mechanism is a constructed by combining a spherical 5R mechanism with a spherical 4R mechanism with distant centers and a common moving link and then removing the common link. This construction allows the analysis and synthesis of the resulting single-loop mechanism by decomposing it into fictitious 5R and 4R loops. The two inputs to the mechanism are provided in the 5R loop and the output is in the 4R loop. The fictitious output of the 5R loop is an input to the 4R loop this intermediate variable is used to also decompose the function to be generated. This decomposition provides the designer extra freedom in synthesis and enables decreasing the error of approximation. A case study is presented at the end of the study where the 7R design is compared with an equivalent spherical 5R mechanism; hence the advantage of the 7R mechanism is demonstrated.

Function Synthesis of the Planar 5R Mechanism Using Least Squares Approximation

In this chapter, the problem of function generation synthesis of planar 5R mechanism is studied using the least squares approximation method with equal spacing of the design points. The study represents a case study for analytical function generation of multi-degrees-of-freedom systems. The planar 5R mechanism is designed with a fixed input joint and a moving input joint adjacent to the first input, whereas the remaining fixed joint is the output joint. The input/output relationship of the mechanism is expreseed as an objective function in polynomial form with four unknown construction parameters. The objective function involves nonlinearities, however the problem is linearized using Lagrange variables. The linear system is solved and finally the construction parameters of the mechanism are determined. A numerical example is presented as a case study.

Trajectory Planning of Redundant Planar Mechanisms for Reducing Task Completion Duration

In the industry there is always a demand to shorten the task completion durations in order to maximize the efficiency of the operation. This work aims to provide a solution to minimize the task completion duration for planar tasks by introducing kinematic redundancy. An example setting of a redundant planar mechanism is considered and an algorithm developed for resolving redundancy order to minimize task completion duration is discussed based on this mechanism.