New Perspectives: Two-Axis Rotations
Students practicing two-axis rotations using blocks.
Students learn about two-axis rotations, and specifically how to rotate objects both physically and mentally about two axes. A two-axis rotation is a rotation of an object about a combination of x, y or z-axes, as opposed to a single-axis rotation, which is about a single x, y or z-axis. Students practice drawing two-axis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangle-dot paper the shapes from various x-, y- and z-axis rotation perspectives. They use the right-hand rule to explore the rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills. At activity end, students re-take the 12-question quiz they took in the associated lesson (before conducting four associated activities) to measure how their spatial visualizations skills improved.
Rotating objects is a spatial visualization technique that enables engineers to visualize complicated assemblies in mechanisms and other systems in a fields such as physics, chemistry, mathematics and engineering. Spatial visualization is an essential and learnable skill that engineers use to clearly communicate their ideas to other people so the ideas can ultimately be turned into real-world products, structures and systems.
Many engineering applications require the depiction of objects from multiple viewpoints, such as mechanical drawings used to manufacture components, architectural drawings, and depictions of chemical compounds. In order to produce these views, an object must be rotated across multiple axes, called two-axis rotations. This skill is similar to lifting up an object and looking at it from all sides, which is not always possible since some objects/components may be too large, heavy or inaccessible for physical manipulation. Instead, engineers must be able to visualize what various viewpoints look like without physically manipulating objects. Typically, engineers use computer-aided design (CAD) software to help visualize complicated rotations of objects. This activity helps students develop two-axis rotation skills.
After this activity, students should be able to:
- Rotate objects about two axes.
- Translate the rotation of one block to a second block.
- Use the right-hand rule to explore rotations of objects.