1) CEREBELLAR HYPOTONIAUnder normal circumstances, the deep cerebellar nuclei send 'reinforcing' signals to the motor cortex and brain stem motor nuclei. This is via the cerebellocortical tract, and serves to increase the tone. Thus, if the deep nuclei are lost for any reason, there is an initial slight decrease in tone. (After a few months though, the motor cortex compensates by increasing its intrinsic activity, and the hypotonia disappears.)

2) LEAD PIPEAs you probably know, this type of rigidity is characteristic of some of the basal ganglial disorders. The causes aren't always known, but in Parkinson's disease, there is loss of dopaminergic neurones of the substantia nigra in the midbrain. In the basal ganglial circuit, dopamine inhibits motor activity, so loss of these inhibitory neurones could cause the spasticity. There would be overactivity of the caudate and putamen, causing a continuously high level of output from the corticospinal tract.

3) COG-WHEELThis is more easily explained - it's simply the superimposition of the tremor on top of the rigidity that produces this sensation.

4) CLASP KNIFEClasp Knife is associated with upper motor neurone lesions, and is actually two phenomena.First, there's the spasticity of the antigravity muscles (muscles of the verebral column and the extensor muscles of the limbs). The antigravity muscles are excited by the pontine reticular nuclei and inhibited by the medullary reticular nuclei (both travel in the reticulospinal tract). Crucially, the medullary portion, unlike the pontine portion, depends heavily on input from the cerebral cortex, red nuclei and basal ganglia. In a stroke, these inputs are lost, and the medullary inhibitor system becomes non-functional, thus allowing full overactivity of the pointine excitatory system. Therefore, spasticity of the antigravity muscles develops.

Second, there's the 'give' (sudden decrease in tone) that occurs after a brief while of rapidly passively extending the muscles. This seems to be an exaggerated response to a normal phenomenon, called the stretch (or myotactic) reflex. Sudden stretching of a muscle is sensed by receptors in the muscle spindles, which cause an initial strong reflex contraction of the muscle concerned. However, this only lasts a brief while, and then is replaced by a much weaker muscular contraction. This system is again dampened by the medullary reticulospinal system, and therefore its loss in a stroke causes the reflex to become exaggerated. Thus, the clasp knife phenomenon is actually a (greatly exaggerated) sudden resistance to contraction, which then subsides after half a second or so, back to baseline spasticity.