Here is an Illustrator tutorial where I will show you to draw a simple icon without using the Pen tool.
Draw the basic shapes
First of all, activate Smart Guides (View > Smart Guides). Pick the Rounded Rectangle Tool and draw a shape as shown above. Modify the corners of the rectangle using the up or down arrow keys while dragging the shape. Make sure that the radius of the rounded corners of the rectangle is big enough. Next, choose the Rectangle Tool and draw a small vertical rectangle shape as shown in the right side of the image. Now, pick the Polygon Tool and draw a small hexagon below the small rectangle (see image above).
Choose the Selection Tool and pick the 3 shapes. From the toolbar, click the Horizontal Align Centre placed at the top. Choose the Direct Selection Tool and drag a selection over the bottom 2 points of the hexagon.
Resizing and aligning the shapes
Click on any one of the points. Hold the Shift key and drag the 2 points downwards as shown in the left side of the image above. Now choose the Selection Tool and pick the small rectangle above the hexagon. Move the cursor to the middle of the bottom border to get the resize cursor icon. To overlap the hexagon shape, drag the border of the rectangle downwards Finalise the grip, merge and align the shapes.
Using the Selection Tool choose both the rectangle and the hexagon. Navigate to the Pathfinder palette. If not visible on the window then go to Window > Pathfinder. Click the Add to shape area option, and then click Expand. Draw a vertical shape using the Rounded Rectangle Tool to finalise the grip of the screwdriver. Modify the radius with the help of the up or down arrows. Use the space bar to move the position of the shape while drawing. Select the shape using the Selection Tool. Duplicate this shape by holding Shift and Option/Alt key while dragging the shape to the right. Choose the grip lines go to Object > Group or hit command/control + g. Now, choose all 3 rounded rectangles and click Horizontal Align Centre from the toolbar.
Select the 3 triangles and navigate to the Pathfinder palette and click on the Subtract from shape area and then on Expand button. Hold the Shift key and select the screwdriver. Group both the shapes into 1: Object > Group or command/control + g. Now we have to draw the wrench. Choose the Ellipse Tool and draw a circle. Draw a rounded rectangle shape on top of the circle using the Rounded Rectangle Tool and as shown in the right-hand side image. Use the up and down arrow keys to modify the corner radius meanwhile you drag the shape. And to move the rectangle while dragging use the spacebar
Using the Selection Tool (black arrow) choose both the rounded rectangle and the circle. Click on the Horizontal Align Centre from the toolbar. Navigate to Pathfinder palette and choose Subtract from shape area. Click the Expand button to expand the object. Choose the Rounded Rectangle Tool and draw a vertical shape for the grip of the wrench. Then pick the Ellipse Tool and draw a small circle (holding down the shift key) at the bottom and on top of the wrench’s grip. Using the Selection Tool choose all the shapes of the wrench and click Horizontal Align Centre.
Choose the small circle and the rounded rectangle. Navigate to Pathfinder palette and choose Subtract from shape area and click the Expand. Now select all shapes of the wrench and click the Add to shape area option, and then click the Expand button.
Rotate and finalise the image
Using the Selection Tool choose the screwdriver. Move around the corners of the selection until you see your cursor changing into a rotation cursor icon. Hold down the mouse and the Shift key at the same time while rotating the object. Release the mouse and the shift key at 90°. The object is now is horizontally placed. Click the Horizontal Align Centre and then the Vertical Align Centre from the toolbar at the top (see right-hand side image above).
Using the Rectangle Tool draw a rectangle shape on top in the centre of both tools as shown. Select both the rectangle and the screwdriver using the Shift key. Navigate to the Pathfinder palette, choose Subtract from shape area and click the Expand button.
Using the Selection Tool, select all the objects. Move the mouse over the selection until you see your cursor changing into a rotation symbol. Hold the mouse and the Shift key to rotate the object. Release the mouse and the shift key at 45° as shown in the image above and you are done!