Abstract
This paper presents a classification scheme of constraints for modeling and simulation of mechanisms and mechanical systems. Current undergraduate kinematic texts deal primarily with pin, slider, cylindrical, ball and a few other types of constraints. Usually other types of constraints and, especially composite constraints are not covered in traditional texts. Only specialized literature deal with composite constraints, and they too are limited to certain types. This paper presents a systematic scheme that is easier to teach, and understand. This scheme is represented by a table that encompasses all types of constraints, and facilitates understanding and developing the constraint equations easily for computer simulation of mechanical systems. In this classification scheme, six constraints (axes, parallel, perpendicular, point, line and plane) have been identified as basic constraint types, and these are then used as building blocks for deriving other constraints. This approach is very effective in modeling mechanical system that can not be modeled just using existing joint types. Furthermore, this building block approach makes it easy to identify suitable composite joints and calculate the degrees of freedom of any joint just by adding the row and the corresponding column number of the classification table. Thus this scheme is very useful in teaching joint types in spatial mechanisms in class rooms. In addition, a mathematical model for each constraint has been constructed using matrix methods making it easier for computer implementation. Constraints or Joints create interconnections between bodies and restrict the relative motion between them in a predetermined fashion. For example, a revolute joint constrains the motion between links to one rotational degree of freedom with respect to a common axis. Currently, the texts by Norton (1992), Erdman and Sandor (1991), Reinholtz and Mabie (1987) and Shigley and Uicker (1981) are widely used for teaching design of machines and mechanisms, and as a reference to practicing engineers. These books provide comprehensive discussion on various joint types and classify joints based on the number of degrees of freedom(dof) permitted/prevented at a joint, the type of contact (point, line, or surface) between the mating elements, or, the type of physical closure (form or force) of the joint. This traditional classification usually covers revolute, prismatic, cylindrical, universal, spherical and a few other joints. Although linkage and several other mechanisms can be modeled using these joints, they do not have the capability to model kinematic constraints necessary to simulate any mechanical system. For example, simulation of the motion of balls in a recirculating ball-screw (or in back-spin game), or, modeling 3-translational motions of a machine tool slide are not directly possible. Thus, in order to model any constraint, composite joints are needed.