Inherently balanced spherical pantograph-based mechanisms

Abstract

Dynamic balancing can offer significant benefits to applications where moving parts are present. It aims to reduce the reaction forces and moments due to inertia of the parts, thereby reducing vibrations. Dynamic balancing receives significant academic interest for planar and spatial applications, but limited attention for spherical mechanisms. This leads to the following goal of this thesis: Present novel force balanced spherical mechanisms design using inherent balancing planar pantograph theory for use in micro precision applications.

To achieve this goal, the thesis has been divided into three sub goals. First is defining the qualitative benefit of dynamic balancing for applications requiring micro-precision. This qualitative analysis looked into six different 'high speed precise' applications with motion and determined a potentially significant benefit exists for applications such as (space) telescopes, space manipulation, additive manufacturing, motions stages and beam steering. Engines and drives require new balancing methods to achieve significant benefit. However, the analysis also showed that many different aspects other then inertia also influence precision, thereby potentially reducing the gained benefit in precision. This is due to the addition of extra components or mass in most common dynamic balancing methods.

The second goal presents five new shaking force balanced spherical mechanisms using inherent balancing theory. Here the planar knowledge of inherently balanced shapes such as the pantograph as well as the use of projections are used to design three novel types of balanced spherical pantographs, namely the spherical pantograph, double spherical pantograph and the double S shaped mechanism with surrounding 4R four-bar linkage. Also, two additional variations of the spherical pantograph and the double spherical pantograph are presented, which leads to a total of five new designs. Each design has its required constraints and available design freedom described. Also, the balance conditions for the double spherical pantograph are presented.

The last goal shows ten novel force balanced remote center mechanisms, using the three types of inherently balanced spherical pantographs. These remote center mechanisms are either using a swivel joint or are a combination of spherical pantographs to form a parallel manipulator. This allows all end effectors to show spherical movement, around a fixed Center of Rotation. The pros and cons as well as feasible variations and constraints are also discussed.
To show the use case of a force balanced remote center mechanism, a realistic design has been made for a beam steering application, where a mirror can perform a tip/tilt movement around a shared center of rotation. The mechanism uses three scaled shifted double spherical pantographs as legs to form a parallel manipulator, with a mirrored surfaced attached to the end effector and positioned in the center of rotation.