### Movement with a Scissor Linkage

The easiest motion to create with the Hummingbird kit is rotation. The gear motors rotate, and the servo motors move in arcs. As students become more experienced, they often want to create other types of motion as well. Linkages can be used to create many different types of motion using the gear and servo motors. For example, students can be challenged to use a linkage to move an object back and  forth.

A linkage is a set of rods or links that are connected by joints. In this project, the links were created from cardboard and connected with brads. One simple type of linkage is a series of connected x’s. This linkage is sometimes called a scissor lift or a pantograph. The scissor linkage can be used with a servo motor. This moves the end of the linkage side to side or back and forth. In this example project, the servo motor was mounted below the table so that the table surface supported the weight of the linkage. The Hummingbird board was powered with a battery pack rather than the AC adapter.

### Drawing with a Scissor Linkage

The scissor linkage can be used in an endless variety of ways! The scissor linkage can also be moved by one or two gear motors. Different patterns of motor movement can produce different paths for the linkage. Attaching a marker to the linkage creates a drawing of the path of a given point. This project was inspired by a drawing machine created by artist Robert Howsare.

Two gear motors are attached to the ends of the linkage. A brad is used to couple each end of the linkage to a wheel attached to the gear motor. This creates a degree of freedom at each attachment point. The linkage cannot be rigidly attached to the gear motors because this would require each end of the linkage to rotate 360°.

A marker attached to the linkage draws the path of a given point. The path can be varied by changing the speed of the motors. The video shows a pattern drawn by several different combinations of motor speeds. If a single combination of motor speeds is used, the system will draw the same path repeatedly. This is shown in the middle image of the picture below.

This project could be extended in many ways. Students could attach more markers and change the speeds of the gear motors to generate different patterns. They could also modify the geometry of the linkage and its attachment to the gear motors. This project could also include reaings of informational texts. For example, students could read an excerpt on the science of linkages from Making Things Move or Mechanisms and Mechanical Devices Sourcebook. Alternatively, students could research the history of the pantograph (a scissor linkage used to copy text and pictures).

Standards:
Linkages are an excellent real-world application of geometry, making them a good fit for Common Core math standard HSG.MG.A. The scissor linkage shown here can be used to discuss similar and congruent shapes (8.G.A, HSG.CO.B, and HSG.SRT.A), as well as theorems concerning vertical angles and parallelograms (HSG.CO.C). In addition, this project aligns with the Next Generation Science Standards for engineering (MS-ETS1-1, MS-ETS1-2, MS-ETS1-3, MS-ETS1-4, HS-ETS1-2, and HS-ETS1-3). Taken further, this project could be used at the university level to enable students to investigate ideas in robot kinematics. If this project includes informational readings, it can also incorporate Common Core ELA standards (anchor standard CCRA.R.10).