Constraint-Based Mechanism Analysis of a Robot Gripper

Journal of Engineering Technology, Fall 2008 by Chen, Daniel

Abstract

This paper discusses the use of a constraint-based design tool to analyze planar mechanisms. A robot gripper was used to demonstrate the technique developed based on the polygon method, focusing on the analyses of position, velocity, acceleration and force. The constraint network provided by the software, which included geometric, dimensional, and algebraic constraints, was utilized to impose relations between vector polygons and skeleton-form mechanism. The technique as developed in this study proved to be much more effective when compared to the traditional graphical or mathematical approach.

I. Introduction

As low-cost, high-speed computing surges, CAD software packages become an integrated part of the engineering world. They are ideal for carrying out twodimensional mechanism analyses. With the constraint network provided by these software packages, constructing a vector polygon that represents a group of velocities, accelerations or forces, relative to different parts in a planar mechanism can be achieved speedily and accurately. This approach eliminates the complex mathematics associated with vector additions in the traditional mathematical approach. 12It also eliminates the laborious manual construction of vector polygons required for the traditional graphical approach,3-4 which is time-consuming yet less accurate. This constraintbased technique should also work well on the synthesis of planar mechanisms.5

The constraint-based design tool utilized in this study is called I-DEAS.6 Three major groups of constraints used include the geometric, dimensional and algebraic. The geometric group includes constraints of coincidence, parallelism, perpendicularity, and location in space. The dimensional group consists of both linear and angular dimensions. The algebraic group uses part equations to relate one dimension to the other. In addition, one of the applied dimensional constraints can be used as a driver to animate the mechanism using the "dimension animation" function in I-DEAS. The associated vector polygon can also be animated as it is properly constrained to the mechanism. Therefore, the change of velocity, acceleration and force through its range of motion can be quickly observed and studied.

The robot gripper of a SCORBOT-ER 3,7 as illustrated in Figure 1, demonstrates the constraint-based technique developed. It consists of the following two popular four-bar mechanisms,8 which commonly can be found in a very wide range of machines and devices:

a) Slider-crank mechanism: It consists of a slider, a connecting rod, and a crank. The input motion to the slider is generated by threaded shaft rotation against a nut in the bearing housing. This drives the double-rocker mechanism that opens or closes the clamp.

b) Double-rocker mechanism: It consists of a pair of parallel rocker arms and a connector. The crank in the slider-crank mechanism drives the inner rocker arm. The clamp, which is an assembly of two triangular plates and a rectangular mounting plate with a rubber cushion, also serves as a connector for the double-rocker mechanism.

The purpose of this study was to develop a constraint-based technique for position, velocity, acceleration, and force analyses. AU the analyses in this study were completed on I-DEAS. However, it is believed that use of any other CAD software would be as successful as long as it is constraint-based.

II. Application of Constraints

Figure 2 shows one of the symmetrical halves, the right half, of the gripper in skeleton form, which includes a slider-crank mechanism at top and a double-rocker mechanism at bottom. Geometric constraints of anchor (Δ) are used as fixed pivots in this case. Both the crank and the inner rocker arm, maintaining a fixed right angle, oscillate about the same fixed pivot. As the slider moves downward, the crank and the inner rocker arm rotate counterclockwise to open the clamp. Geometric constraints enforce relationships between different lines of a skeleton with internally written equations that force the given geometric relationships to be true.9 Other geometric constraints, including parallel Cf) and perpendicular (JL), are applied to ensure that the inner and outer rocker arms move in parallel and that the slider's shape and size are always constant. A midpoint constraint (0) is applied to the lower edge of the slider to ensure its center is pinned to the connecting rod.

Figure 3 shows a fully constrained skeleton with all the required constraints in place. In addition to the geometric constraints, a number of dimensional constraints, in millimeters and degrees of angle, are applied to the skeleton. Dimensional constraints are essentially equations where the given value is set equal to a constant that can be modified later. A fully constrained skeleton attains the maximum number of constraints. There could be more than one possible solution if fewer than this number are applied and a change is made to a value. Figure 3 shows a number of geometric constraints which can not be found in Figure 2. These are needed to permit the skeleton to function like a gripper mechanism. They include an anchor on the dotted vertical line to ensure it remains stationary and a parallel constraint to force the slider in motion to maintain its orientation relative to the horizontal ground (between the two fixed pivots) at all times.